{"id":1248,"date":"2026-11-09T18:52:57","date_gmt":"2026-11-09T18:52:57","guid":{"rendered":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/?p=1248"},"modified":"2026-11-10T06:30:32","modified_gmt":"2026-11-10T06:30:32","slug":"quadrilaterals","status":"publish","type":"post","link":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/11\/09\/quadrilaterals\/","title":{"rendered":"\u0905\u0927\u094d\u092f\u093e\u092f 12: \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c"},"content":{"rendered":"<div id=\"pl-1248\"  class=\"panel-layout\" ><div id=\"pg-1248-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-1248-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-1248-0-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"0\" ><div class=\"textwidget custom-html-widget\"><div class=\"pargai-multislider\">\n    <div class=\"slider-header-section\">\n        <div class=\"header-main-title\">\u092d\u093e\u0917 1: \u0905\u0927\u094d\u092f\u093e\u092f 12 - \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c (\u092a\u0930\u093f\u091a\u092f)<\/div>\n    <\/div>\n    \n    <div class=\"slider-content-area\">\n        <div class=\"pargai-slide active-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 1: \u0905\u0927\u094d\u092f\u093e\u092f \u0915\u0940 \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e:<\/b><\/p>\n            <p>\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c (\u092f\u093e 4-\u092d\u0941\u091c \/ 4-gon) \u0939\u092e\u093e\u0930\u0947 \u0926\u0948\u0928\u093f\u0915 \u091c\u0940\u0935\u0928 \u092e\u0947\u0902 \u0939\u0930 \u091c\u0917\u0939 \u092a\u093e\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902, \u091c\u0948\u0938\u0947 \u0935\u0930\u094d\u0917\u093e\u0915\u093e\u0930 \u091f\u093e\u0907\u0932\u094b\u0902 \u0938\u0947 \u092b\u0930\u094d\u0936 \u0915\u0940 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 (Tiling) \u0915\u0930\u0928\u093e[cite: 21]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 2: \u0938\u092e\u0924\u0932 \u0915\u0940 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 (Tiling the Plane):<\/b><\/p>\n            <p>\u0915\u093f\u0938\u0940 \u0938\u092e\u0924\u0932 \u0915\u094b \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u0905\u0902\u0924\u0930\u093e\u0932 (gaps) \u092f\u093e \u0905\u0924\u093f\u0935\u094d\u092f\u093e\u092a\u0928 (overlaps) \u0915\u0947 \u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902 \u0938\u0947 \u0922\u0915\u0928\u093e \u091f\u093e\u0907\u0932\u093f\u0902\u0917 \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948[cite: 21]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 3: \u0932\u0915\u0921\u093c\u0940 \u0915\u0947 \u091b\u0921\u093c\u094b\u0902 \u0915\u093e \u0917\u094d\u0930\u093f\u0921:<\/b><\/p>\n            <p>\u092f\u0926\u093f \u0939\u092e \u0906\u092f\u0924\u093e\u0915\u093e\u0930 \u0917\u094d\u0930\u093f\u0921 \u0915\u094b \u0925\u094b\u0921\u093c\u093e \u091d\u0941\u0915\u093e \u0926\u0947\u0902, \u0924\u094b \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c (Parallelogram) \u092c\u0928\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0928\u0915\u0940 \u0938\u0939\u093e\u092f\u0924\u093e \u0938\u0947 \u0938\u092e\u0924\u0932 \u0915\u094b \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0922\u0915\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948[cite: 21, 22]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 4: \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u091f\u0940\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e:<\/b><\/p>\n            <p>\u0938\u0939\u091c \u0930\u0942\u092a \u0938\u0947 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u091a\u093e\u0930 \u0938\u0940\u0927\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0935\u093e\u0932\u0940 \u0906\u0915\u0943\u0924\u093f \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0938\u094d\u0935-\u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926\u0940 \u0914\u0930 \u0917\u0948\u0930-\u0938\u092e\u0924\u0932\u0940\u092f \u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u0924\u0930\u094d\u0915\u0924\u093e \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948[cite: 22, 23]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 5: \u0909\u0924\u094d\u0924\u0932 (Convex) \u0914\u0930 \u0905\u0935\u0924\u0932 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c:<\/b><\/p>\n            <p>\u091c\u093f\u0938 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u092e\u0947\u0902 \u0915\u094b\u0908 '\u0921\u0947\u0902\u091f' \u0928 \u0939\u094b \u0914\u0930 \u0938\u092d\u0940 \u0906\u0902\u0924\u0930\u093f\u0915 \u0915\u094b\u0923 180&deg; \u0938\u0947 \u0915\u092e \u0939\u094b\u0902, \u0909\u0938\u0947 \u0909\u0924\u094d\u0924\u0932 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0924\u0925\u093e \u0905\u0928\u094d\u092f\u0925\u093e \u0905\u0935\u0924\u0932 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0939\u0924\u0947 \u0939\u0948\u0902[cite: 24]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 6: \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u0932\u093f\u0902\u0915\u0947\u091c (Mechanical Linkages):<\/b><\/p>\n            <p>\u0907\u0902\u091c\u0940\u0928\u093f\u092f\u0930\u093f\u0902\u0917 \u092e\u0947\u0902 \u092b\u094b\u0930-\u092c\u093e\u0930 \u0932\u093f\u0902\u0915\u0947\u091c \u091c\u0948\u0938\u0940 \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0917\u0948\u0930-\u0909\u0924\u094d\u0924\u0932 \u0914\u0930 \u0938\u094d\u0935-\u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u091c\u0940\u0935\u0928 \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902[cite: 25]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 7: \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917:<\/b><\/p>\n            <p>\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u092c\u0939\u0941\u0924 \u0939\u0940 \u092c\u0939\u0941\u092e\u0941\u0916\u0940 \u0906\u0915\u0943\u0924\u093f\u092f\u093e\u0901 \u0939\u0948\u0902, \u091c\u093f\u0928\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u092d\u094c\u0924\u093f\u0915\u0940 (\u092c\u0932\u094b\u0902 \u0915\u0947 \u0938\u0902\u092f\u094b\u091c\u0928) \u0914\u0930 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u0909\u092a\u0915\u0930\u0923\u094b\u0902 (\u091c\u0948\u0938\u0947 \u092a\u0948\u0902\u091f\u094b\u0917\u094d\u0930\u093e\u092b) \u092e\u0947\u0902 \u0939\u094b\u0924\u093e \u0939\u0948[cite: 30, 31]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 8: \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0917\u0941\u0923:<\/b><\/p>\n            <p>\u0907\u0938 \u0905\u0927\u094d\u092f\u093e\u092f \u0915\u0947 \u0909\u0924\u094d\u0924\u0930\u093e\u0930\u094d\u0927 \u092e\u0947\u0902 \u0939\u092e \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u092e\u0926\u0926 \u0938\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f (Midpoint Theorem) \u0914\u0930 \u0915\u0947\u0902\u0926\u094d\u0930\u0915 (Centroid) \u0915\u094b \u0938\u092e\u091d\u0947\u0902\u0917\u0947[cite: 31, 33, 36]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 9: Varignon \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f:<\/b><\/p>\n            <p>\u0915\u093f\u0938\u0940 \u092d\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u091a\u093e\u0930\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u0906\u092a\u0938 \u092e\u0947\u0902 \u092e\u093f\u0932\u093e\u0928\u0947 \u092a\u0930 \u0939\u092e\u0947\u0936\u093e \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c (Varignon Parallelogram) \u092c\u0928\u0924\u093e \u0939\u0948[cite: 37]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 10: \u0905\u0927\u094d\u092f\u093e\u092f \u0915\u093e \u092e\u0941\u0916\u094d\u092f \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f:<\/b><\/p>\n            <p>\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0914\u0930 \u0935\u093f\u0936\u0947\u0937\u0915\u0930 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u0917\u0941\u0923\u094b\u0902, \u0909\u0928\u0915\u0940 \u091c\u093e\u0901\u091a \u0915\u0947 \u0924\u0930\u0940\u0915\u094b\u0902 \u0914\u0930 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u092e\u0947\u0902 \u0909\u0928\u0915\u0947 \u0936\u0915\u094d\u0924\u093f\u0936\u093e\u0932\u0940 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u0915\u094b \u0938\u0940\u0916\u0928\u093e \u0907\u0938 \u0905\u0927\u094d\u092f\u093e\u092f \u0915\u093e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u0939\u0948[cite: 22]\u3002<\/p>\n        <\/div>\n    <\/div>\n\n    <div class=\"slider-footer-section\">\n        <button class=\"slider-nav-btn btn-prev\">\u092a\u093f\u091b\u0932\u093e (Prev)<\/button>\n        <span class=\"slider-page-counter\">1 \/ 10<\/span>\n        <button class=\"slider-nav-btn btn-next\">\u0905\u0917\u0932\u093e (Next)<\/button>\n    <\/div>\n<\/div><\/div><\/div><\/div><\/div><div id=\"pg-1248-1\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-1248-1-0\"  class=\"panel-grid-cell\" ><div id=\"panel-1248-1-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"1\" ><div class=\"textwidget custom-html-widget\"><div class=\"pargai-multislider\">\n    <div class=\"slider-header-section\">\n        <div class=\"header-main-title\">\u092d\u093e\u0917 2: \u0905\u0927\u094d\u092f\u093e\u092f 12 - \u092e\u0941\u0916\u094d\u092f \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0914\u0930 \u0928\u093f\u092f\u092e<\/div>\n    <\/div>\n    \n    <div class=\"slider-content-area\">\n        <div class=\"pargai-slide active-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 1: \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/b><\/p>\n            <p>\u0938\u092e\u0924\u0932 \u092e\u0947\u0902 \u091a\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 A, B, C, D \u0915\u0947 \u0916\u0902\u0921\u094b\u0902 AB, BC, CD \u0914\u0930 DA \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u092c\u093f\u0902\u0926\u0941 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ABCD \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902, \u092c\u0936\u0930\u094d\u0924\u0947 \u0915\u094b\u0908 \u092d\u0940 \u0924\u0940\u0928 \u092c\u093f\u0902\u0926\u0941 \u0938\u0902\u0930\u0947\u0916 \u0928 \u0939\u094b\u0902[cite: 23]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 2: \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u092e\u0942\u0932 \u0917\u0941\u0923 (Theorem 1):<\/b><\/p>\n            <p>(a) \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u090f\u0901 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964 (b) \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 (c) \u0935\u093f\u0915\u0930\u094d\u0923 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902[cite: 26]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 3: \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0932\u094b\u092e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 (Theorems 2, 3, 4):<\/b><\/p>\n            <p>\u092f\u0926\u093f \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u090f\u0901 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0902, \u092f\u093e \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0902, \u0905\u0925\u0935\u093e \u0935\u093f\u0915\u0930\u094d\u0923 \u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0947\u0902, \u0924\u094b \u0935\u0939 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948[cite: 28, 29]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 4: \u0938\u092e\u093e\u0928 \u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 (Theorem 5):<\/b><\/p>\n            <p>\u091c\u093f\u0938 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u092e\u0947\u0902 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930 \u0939\u094b, \u0935\u0939 \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948[cite: 29]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 5: \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f (Theorem 6):<\/b><\/p>\n            <p>\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0915\u093f\u0928\u094d\u0939\u0940\u0902 \u0926\u094b \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u093e \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0914\u0930 \u0932\u0902\u092c\u093e\u0908 \u0915\u093e \u0906\u0927\u093e \u0939\u094b\u0924\u093e \u0939\u0948[cite: 33]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 6: \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0935\u093f\u0932\u094b\u092e (Theorem 7):<\/b><\/p>\n            <p>\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u090f\u0915 \u092d\u0941\u091c\u093e \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u0942\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0916\u0940\u0902\u091a\u0940 \u0917\u0908 \u0930\u0947\u0916\u093e \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948[cite: 34]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 7: \u0915\u0947\u0902\u0926\u094d\u0930\u0915 \u092a\u094d\u0930\u092e\u0947\u092f (Centroid Theorem - Theorem 8):<\/b><\/p>\n            <p>\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0924\u0940\u0928\u094b\u0902 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e\u090f\u0901 \u0938\u0902\u0917\u093e\u092e\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902 \u0914\u0930 \u0915\u0947\u0902\u0926\u094d\u0930\u0915 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0915\u094b 2:1 \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 (\u0936\u0940\u0930\u094d\u0937 \u0915\u0940 \u0913\u0930 \u092c\u0921\u093c\u093e \u092d\u093e\u0917)[cite: 36]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 8: Varignon \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f (Theorem 9):<\/b><\/p>\n            <p>\u0915\u093f\u0938\u0940 \u092d\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u091a\u093e\u0930\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0938\u0947 \u092c\u0928\u0928\u0947 \u0935\u093e\u0932\u0940 \u0906\u0915\u0943\u0924\u093f \u0939\u092e\u0947\u0936\u093e \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u0940 \u0939\u0948[cite: 37]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 9: \u0938\u092e\u0932\u0902\u092c \u0914\u0930 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0938\u0902\u092c\u0902\u0927:<\/b><\/p>\n            <p>\u0938\u092e\u0932\u0902\u092c (Trapezium) \u092e\u0947\u0902 \u0917\u0948\u0930-\u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u0940 \u0906\u0927\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948[cite: 47]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 10: \u092c\u0939\u0941\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0915\u093e \u0938\u0942\u0924\u094d\u0930:<\/b><\/p>\n            <p>n \u092d\u0941\u091c\u093e\u0913\u0902 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092d\u0941\u091c \u092e\u0947\u0902 \u0915\u0941\u0932 \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u092e\u093e\u0928\u0915 \u0938\u0942\u0924\u094d\u0930 n(n - 3) \/ 2 \u0939\u094b\u0924\u093e \u0939\u0948[cite: 51]\u3002<\/p>\n        <\/div>\n    <\/div>\n\n    <div class=\"slider-footer-section\">\n        <button class=\"slider-nav-btn btn-prev\">\u092a\u093f\u091b\u0932\u093e (Prev)<\/button>\n        <span class=\"slider-page-counter\">1 \/ 10<\/span>\n        <button class=\"slider-nav-btn btn-next\">\u0905\u0917\u0932\u093e (Next)<\/button>\n    <\/div>\n<\/div><\/div><\/div><\/div><\/div><div id=\"pg-1248-2\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-1248-2-0\"  class=\"panel-grid-cell\" ><div id=\"panel-1248-2-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"2\" ><div class=\"textwidget custom-html-widget\"><div class=\"pargai-multislider\">\n    <div class=\"slider-header-section\">\n        <div class=\"header-main-title\">\u092d\u093e\u0917 3: \u0905\u0927\u094d\u092f\u093e\u092f 12 - \u0905\u092d\u094d\u092f\u093e\u0938 \u0914\u0930 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0939\u0932 (Exercise Solutions)<\/div>\n    <\/div>\n    \n    <div class=\"slider-content-area\">\n        <div class=\"pargai-slide active-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 1: Exercise Set 12.1 (\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0905\u0902\u0917 \u0914\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093e):<\/b><\/p>\n            <p><b>\u092a\u094d\u0930\u0936\u094d\u0928 1-3:<\/b> \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ABCD \u092e\u0947\u0902 \u092d\u0941\u091c\u093e AB \u0915\u0940 \u0906\u0938\u0928\u094d\u0928 \u092d\u0941\u091c\u093e\u090f\u0901 AD \u0914\u0930 BC \u0924\u0925\u093e \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e DC \u0939\u0948[cite: 25, 26]\u0964 \u0906\u0902\u0924\u0930\u093f\u0915 \u0915\u094b\u0923\u094b\u0902, \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0914\u0930 \u0905\u0935\u0924\u0932\/\u0909\u0924\u094d\u0924\u0932 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 (\u091c\u0948\u0938\u0947 AB || DC \u0939\u094b\u0928\u0947 \u092a\u0930 \u0936\u0930\u094d\u0924\u0947\u0902) \u0915\u093e \u0938\u091f\u0940\u0915 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948[cite: 24, 26]\u0964<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 2: Exercise Set 12.2 (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0917\u0941\u0923):<\/b><\/p>\n            <p><b>\u092a\u094d\u0930\u0936\u094d\u0928 1-2:<\/b> (i) \u0938\u092e\u0915\u094b\u0923 \u0935\u093e\u0932\u093e \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0906\u092f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 (\u0938\u0924\u094d\u092f)\u0964 (ii) \u0932\u0902\u092c\u0935\u0924 \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0935\u093e\u0932\u093e \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0935\u0930\u094d\u0917 \u0939\u094b\u0924\u093e \u0939\u0948 (\u0938\u0924\u094d\u092f)\u0964 (iii) \u092f\u0926\u093f \u0935\u093f\u0915\u0930\u094d\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0902 \u0924\u094b \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0906\u092f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948[cite: 30]\u0964 \u0935\u093f\u0915\u0930\u094d\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u094b\u0923 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0939\u094b\u0928\u0947 \u092a\u0930 \u0909\u0938\u0947 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e[cite: 30]\u0964<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 3: Exercise Set 12.2 (\u092a\u094d\u0930\u0936\u094d\u0928 3 & 4 - \u0935\u093f\u0932\u094b\u092e \u0914\u0930 \u0915\u094b\u0923 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915):<\/b><\/p>\n            <p><b>\u092a\u094d\u0930\u0936\u094d\u0928 3-4:<\/b> \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0915\u0947 \u0915\u094b\u0923 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0928, \u0932\u0902\u092c\u0935\u0924 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0928 \u0914\u0930 \u0938\u092e\u093e\u0928 \u0932\u0902\u092c\u093e\u0908 \u0915\u0947 \u0935\u093f\u0932\u094b\u092e \u0915\u0925\u0928\u094b\u0902 \u0915\u0940 \u091c\u093e\u0901\u091a[cite: 30]\u0964 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u091a\u093e\u0930\u094b\u0902 \u0915\u094b\u0923\u094b\u0902 \u0915\u0947 \u0906\u0902\u0924\u0930\u093f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0915\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926\u0928 \u092c\u093f\u0902\u0926\u0941 \u090f\u0915 \u0906\u092f\u0924 \u092c\u0928\u093e\u0924\u093e \u0939\u0948[cite: 30]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 4: Exercise Set 12.3 (\u092a\u094d\u0930\u0936\u094d\u0928 1 & 2 - \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917):<\/b><\/p>\n            <p><b>\u092a\u094d\u0930\u0936\u094d\u0928 1-2:<\/b> \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0938\u0947 \u092c\u0928\u0928\u0947 \u0935\u093e\u0932\u0947 \u091a\u093e\u0930 \u091b\u094b\u091f\u0947 \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0914\u0930 \u092a\u0941\u0928\u0930\u094d\u0928\u093f\u0930\u094d\u092e\u093e\u0923[cite: 37, 38]\u0964 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 M \u0914\u0930 N \u0938\u0947 \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0926\u094d\u0935\u093e\u0930\u093e AD \u0915\u0947 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e[cite: 38]\u0964<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 5: Exercise Set 12.3 (\u092a\u094d\u0930\u0936\u094d\u0928 3, 4 & 5 - Varignon \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c):<\/b><\/p>\n            <p><b>\u092a\u094d\u0930\u0936\u094d\u0928 3-5:<\/b> \u091f\u094d\u0930\u0948\u092a\u0947\u091c\u093c\u093f\u092f\u092e \u092e\u0947\u0902 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0938\u0947 \u092c\u0928\u0940 \u0930\u0947\u0916\u093e \u0915\u093e \u0906\u0927\u093e\u0930 \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0939\u094b\u0928\u093e[cite: 38]\u0964 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0938\u0947 \u092c\u0928\u0947 Varignon \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c PQRS \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0915\u093e \u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0928\u093e \u0914\u0930 AC = BD \u0939\u094b\u0928\u0947 \u092a\u0930 \u0932\u0902\u092c\u0935\u0924 \u0939\u094b\u0928\u093e[cite: 38]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 6: Exercise Set 12.4 (\u091f\u093e\u0907\u0932\u093f\u0902\u0917 \u0914\u0930 \u092a\u0948\u091f\u0930\u094d\u0928):<\/b><\/p>\n            <p><b>\u092a\u094d\u0930\u0936\u094d\u0928 1-2:<\/b> \u0928\u093f\u092f\u092e\u093f\u0924 \u092a\u0902\u091a\u092d\u0941\u091c (Regular Pentagon) \u0938\u0947 \u0938\u092e\u0924\u0932 \u0915\u0940 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 \u0915\u094d\u092f\u094b\u0902 \u0938\u0902\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948, \u0907\u0938\u0915\u093e \u0914\u091a\u093f\u0924\u094d\u092f (\u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0915\u094b\u0923 360&deg; \u0915\u094b \u092a\u0942\u0930\u093e \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u093e)\u0964 \u0917\u0948\u0930-\u0909\u0924\u094d\u0924\u0932 4-gon (DART) \u0938\u0947 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 \u0915\u0940 \u0935\u093f\u0927\u093f\u092f\u093e\u0901\u0964<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 7: End-of-Chapter (\u092a\u094d\u0930\u0936\u094d\u0928 1 - 4 - \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c):<\/b><\/p>\n            <p><b>\u092a\u094d\u0930\u0936\u094d\u0928 1-4:<\/b> \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0917\u0941\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u0947 \u0938\u092e\u0924\u0932 \u0915\u0940 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 \u0915\u0930\u0928\u093e\u0964 \u0938\u094d\u0935-\u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917\u0964 \u0935\u093f\u0915\u0930\u094d\u0923 BD \u092a\u0930 \u092c\u093f\u0902\u0926\u0941 P \u0914\u0930 Q ($DP = BQ$) \u0939\u094b\u0928\u0947 \u092a\u0930 $APCQ$ \u0915\u093e \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0928\u093e\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 8: End-of-Chapter (\u092a\u094d\u0930\u0936\u094d\u0928 5 - 9 - \u0938\u092e\u0932\u0902\u092c \u0914\u0930 \u0924\u094d\u0930\u093f\u092d\u093e\u091c\u0928):<\/b><\/p>\n            <p><b>\u092a\u094d\u0930\u0936\u094d\u0928 5-9:<\/b> \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u092e\u094b\u0921\u093c\u0928\u0947 \u092a\u0930 \u0915\u094d\u0930\u0940\u091c \u0926\u094d\u0935\u093e\u0930\u093e \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u093e\u0964 \u0938\u092e\u0932\u0902\u092c (Trapezium) \u092e\u0947\u0902 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u093e\u0930 $EF = \\frac{AB + CD}{2}$\u0964 \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926\u0928 \u0914\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0940 \u0917\u0923\u0928\u093e\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 9: End-of-Chapter (\u092a\u094d\u0930\u0936\u094d\u0928 10 - 24 - \u092c\u0939\u0941\u092d\u0941\u091c \u0938\u0942\u0924\u094d\u0930 \u0914\u0930 \u0917\u0941\u0923):<\/b><\/p>\n            <p><b>\u092a\u094d\u0930\u0936\u094d\u0928 10-24:<\/b> 4 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0938\u0947 \u092c\u0928\u0928\u0947 \u0935\u093e\u0932\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u094b\u0902 \u0915\u0940 \u0917\u093f\u0928\u0924\u0940\u0964 $n$ \u092d\u0941\u091c\u093e\u0913\u0902 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092d\u0941\u091c \u0915\u0947 \u0915\u0941\u0932 \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e $\\frac{n(n-3)}{2}$ \u0914\u0930 \u0905\u0902\u0924\u0903\u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 $(n-2) \\times 180&deg;$\u0964 \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0915\u093e \u0924\u094d\u0930\u093f\u092d\u093e\u091c\u0928 (Trisection)\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 10: \u0905\u092d\u094d\u092f\u093e\u0938 \u0938\u093e\u0930\u093e\u0902\u0936 \u0914\u0930 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937:<\/b><\/p>\n            <p><b>\u0905\u0927\u094d\u092f\u093e\u092f \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937:<\/b> \u0907\u0928 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0905\u092d\u094d\u092f\u093e\u0938\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0939\u092e \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u0935\u0930\u094d\u0917\u0940\u0915\u0930\u0923, \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0915\u0938\u094c\u091f\u093f\u092f\u094b\u0902, \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f\u094b\u0902 (Midpoint Theorems), \u0914\u0930 \u0938\u092e\u0924\u0932 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924\u094b\u0902 \u092e\u0947\u0902 \u092a\u0942\u0930\u0940 \u0924\u0930\u0939 \u092a\u093e\u0930\u0902\u0917\u0924 \u0939\u094b \u091c\u093e\u0924\u0947 \u0939\u0948\u0902[cite: 33, 37]\u3002<\/p>\n        <\/div>\n    <\/div>\n\n    <div class=\"slider-footer-section\">\n        <button class=\"slider-nav-btn btn-prev\">\u092a\u093f\u091b\u0932\u093e (Prev)<\/button>\n        <span class=\"slider-page-counter\">1 \/ 10<\/span>\n        <button class=\"slider-nav-btn btn-next\">\u0905\u0917\u0932\u093e (Next)<\/button>\n    <\/div>\n<\/div><\/div><\/div><\/div><\/div><div id=\"pg-1248-3\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-1248-3-0\"  class=\"panel-grid-cell\" ><div id=\"panel-1248-3-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"3\" ><div class=\"textwidget custom-html-widget\"><div class=\"pargai-multislider\">\n    <div class=\"slider-header-section\">\n        <div class=\"header-main-title\">\u092d\u093e\u0917 4: \u0905\u0927\u094d\u092f\u093e\u092f 12 - \u0930\u093f\u0935\u093f\u091c\u0928 \u0914\u0930 \u0938\u093e\u0930\u093e\u0902\u0936<\/div>\n    <\/div>\n    \n    <div class=\"slider-content-area\">\n        <div class=\"pargai-slide active-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 1: \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u092e\u0942\u0932 \u0905\u0935\u0927\u093e\u0930\u0923\u093e:<\/b><\/p>\n            <p>\u091a\u093e\u0930 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0938\u0947 \u092c\u0928\u0940 \u0938\u092e\u0924\u0932, \u0917\u0948\u0930-\u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926\u0940 \u0906\u0915\u0943\u0924\u093f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0939\u0932\u093e\u0924\u0940 \u0939\u0948, \u091c\u093f\u0938\u0915\u0947 \u0938\u092d\u0940 \u0905\u0902\u0924\u0903\u0915\u094b\u0923 \u0909\u0924\u094d\u0924\u0932 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 180&deg; \u0938\u0947 \u0915\u092e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902[cite: 53]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 2: \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0940 \u0915\u0938\u094c\u091f\u093f\u092f\u093e\u0901:<\/b><\/p>\n            <p>\u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u090f\u0901 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0902, \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0902, \u0935\u093f\u0915\u0930\u094d\u0923 \u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0947\u0902, \u092f\u093e \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u090f\u0935\u0902 \u0938\u092e\u093e\u0902\u0924\u0930 \u0939\u094b[cite: 53]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 3: \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f (Midpoint Theorem):<\/b><\/p>\n            <p>\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0926\u094b \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u093e \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0914\u0930 \u0906\u0927\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 4: \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0935\u093f\u0932\u094b\u092e:<\/b><\/p>\n            <p>\u090f\u0915 \u092d\u0941\u091c\u093e \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0916\u0940\u0902\u091a\u0940 \u0917\u0908 \u0938\u092e\u093e\u0902\u0924\u0930 \u0930\u0947\u0916\u093e \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 5: \u0915\u0947\u0902\u0926\u094d\u0930\u0915 (Centroid) \u0914\u0930 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e\u090f\u0901:<\/b><\/p>\n            <p>\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0924\u0940\u0928\u094b\u0902 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e\u090f\u0901 \u0938\u0902\u0917\u093e\u092e\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902 \u0914\u0930 \u0915\u0947\u0902\u0926\u094d\u0930\u0915 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0915\u094b 2:1 \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 6: Varignon \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c:<\/b><\/p>\n            <p>\u0915\u093f\u0938\u0940 \u092d\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u091a\u093e\u0930\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0938\u0947 \u0939\u092e\u0947\u0936\u093e \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0939\u094b\u0924\u093e \u0939\u0948\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 7: \u0938\u092e\u0924\u0932 \u0915\u0940 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 (Tiling):<\/b><\/p>\n            <p>\u0915\u093f\u0938\u0940 \u092d\u0940 \u0905\u0928\u093f\u092f\u092e\u093f\u0924 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c (4-gon) \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0938\u092e\u0924\u0932 \u0915\u094b \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0947 \u092a\u0942\u0930\u0940 \u0924\u0930\u0939 \u0922\u0915\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948[cite: 40]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 8: \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0914\u0930 \u0915\u094b\u0923\u094b\u0902 \u0915\u0947 \u0938\u0902\u092c\u0902\u0927:<\/b><\/p>\n            <p>\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u091a\u093e\u0930\u094b\u0902 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u0939\u092e\u0947\u0936\u093e 360&deg; \u0939\u094b\u0924\u093e \u0939\u0948, \u091a\u093e\u0939\u0947 \u0935\u0939 \u0909\u0924\u094d\u0924\u0932 \u0939\u094b \u092f\u093e \u0905\u0935\u0924\u0932[cite: 45]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 9: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0924\u0930\u094d\u0915 \u0914\u0930 \u0935\u093f\u0932\u094b\u092e:<\/b><\/p>\n            <p>\u092a\u094d\u0930\u092e\u0947\u092f\u094b\u0902 \u0915\u0947 \u0935\u093f\u0932\u094b\u092e \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0924\u0947 \u0938\u092e\u092f \u0909\u091a\u093f\u0924 \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0914\u091a\u093f\u0924\u094d\u092f \u0926\u0947\u0928\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948[cite: 28]\u3002<\/p>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 10: \u0905\u0927\u094d\u092f\u093e\u092f \u0915\u093e \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937:<\/b><\/p>\n            <p>\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0917\u0941\u0923 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0914\u0930 \u0906\u0927\u0941\u0928\u093f\u0915 \u0921\u093f\u091c\u093e\u0907\u0928\u094b\u0902 \u0935 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u093e \u0906\u0927\u093e\u0930 \u0939\u0948\u0902[cite: 22, 30]\u3002<\/p>\n        <\/div>\n    <\/div>\n\n    <div class=\"slider-footer-section\">\n        <button class=\"slider-nav-btn btn-prev\">\u092a\u093f\u091b\u0932\u093e (Prev)<\/button>\n        <span class=\"slider-page-counter\">1 \/ 10<\/span>\n        <button class=\"slider-nav-btn btn-next\">\u0905\u0917\u0932\u093e (Next)<\/button>\n    <\/div>\n<\/div><\/div><\/div><\/div><\/div><div id=\"pg-1248-4\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-1248-4-0\"  class=\"panel-grid-cell\" ><div id=\"panel-1248-4-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"4\" ><div class=\"textwidget custom-html-widget\"><div class=\"pargai-multislider\">\n    <div class=\"slider-header-section\">\n        <div class=\"header-main-title\">\u092d\u093e\u0917 5: \u0905\u0927\u094d\u092f\u093e\u092f 12 - \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 \u0935\u093f\u0936\u0947\u0937 \u0905\u092d\u094d\u092f\u093e\u0938 \u092c\u094d\u0932\u0949\u0915 (MCQ Format)<\/div>\n    <\/div>\n    \n    <div class=\"slider-content-area\">\n        <div class=\"pargai-slide active-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 1: \u0935\u0930\u094d\u0917 \u0914\u0930 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u094b \u0938\u092e\u0915\u094b\u0923 \u092a\u0930 \u0915\u093e\u091f\u0947\u0902 \u0914\u0930 \u0906\u092a\u0938 \u092e\u0947\u0902 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0902, \u0924\u094b \u0935\u0939 \u0906\u0915\u0943\u0924\u093f \u0915\u094d\u092f\u093e \u0915\u0939\u0932\u093e\u0924\u0940 \u0939\u0948?<br>\n            (a) \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<br>(b) \u0906\u092f\u0924<br>(c) \u0935\u0930\u094d\u0917<br>(d) \u0938\u092e\u0932\u0902\u092c<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (c) \u0935\u0930\u094d\u0917 (Square)<\/b><\/div>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 2: \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u0947\u0902\u0926\u094d\u0930\u0915:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u0915\u093f\u0938\u0940 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0924\u0940\u0928\u094b\u0902 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e\u0913\u0902 \u0915\u0947 \u0915\u091f\u093e\u0928 \u092c\u093f\u0902\u0926\u0941 \u0915\u094b \u0915\u094d\u092f\u093e \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092f\u0939 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0915\u094b \u0915\u093f\u0938 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948?<br>\n            (a) \u0932\u0902\u092c \u0915\u0947\u0902\u0926\u094d\u0930, 1:1<br>(b) \u0915\u0947\u0902\u0926\u094d\u0930\u0915, 2:1 (\u0936\u0940\u0930\u094d\u0937 \u0915\u0940 \u0913\u0930)<br>(c) \u0905\u0902\u0924\u0903\u0915\u0947\u0902\u0926\u094d\u0930, 3:2<br>(d) \u092a\u0930\u093f\u0915\u0947\u0902\u0926\u094d\u0930, 1:2<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (b) \u0915\u0947\u0902\u0926\u094d\u0930\u0915, 2:1<\/b>[cite: 36]<\/div>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 3: Varignon \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u092f\u093e \u0905\u0928\u093f\u092f\u092e\u093f\u0924 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u091a\u093e\u0930\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u092a\u0930 \u0915\u094c\u0928 \u0938\u0940 \u0906\u0915\u0943\u0924\u093f \u092c\u0928\u0924\u0940 \u0939\u0948?<br>\n            (a) \u0906\u092f\u0924<br>(b) \u0935\u0930\u094d\u0917<br>(c) \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<br>(d) \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (c) \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c (Varignon Parallelogram)<\/b>[cite: 37]<\/div>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 4: \u0938\u092e\u0932\u0902\u092c \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0905\u092d\u094d\u092f\u093e\u0938:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u090f\u0915 \u0938\u092e\u0932\u0902\u092c \u0915\u0940 \u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u090f\u0901 3 \u0938\u0947\u092e\u0940 \u0914\u0930 5 \u0938\u0947\u092e\u0940 \u0939\u0948\u0902\u0964 \u0907\u0938\u0915\u0940 \u0917\u0948\u0930-\u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u0940?<br>\n            (a) 3 \u0938\u0947\u092e\u0940<br>(b) 4 \u0938\u0947\u092e\u0940<br>(c) 5 \u0938\u0947\u092e\u0940<br>(d) 8 \u0938\u0947\u092e\u0940<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (b) 4 \u0938\u0947\u092e\u0940<\/b>[cite: 47]<\/div>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 5: \u092c\u0939\u0941\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u0937\u0921\u094d\u092d\u0941\u091c (Hexagon, n=6) \u092e\u0947\u0902 \u0915\u0941\u0932 \u0915\u093f\u0924\u0928\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902?<br>\n            (a) 6<br>(b) 9<br>(c) 12<br>(d) 15<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (b) 9 \u0935\u093f\u0915\u0930\u094d\u0923<\/b>[cite: 51]<\/div>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 6: \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u0915\u093f\u0938\u0940 \u092d\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u091a\u093e\u0930\u094b\u0902 \u0906\u0902\u0924\u0930\u093f\u0915 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u0915\u093f\u0924\u0928\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<br>\n            (a) 180&deg;<br>(b) 270&deg;<br>(c) 360&deg;<br>(d) 540&deg;<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (c) 360&deg;<\/b>[cite: 45]<\/div>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 7: \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u092a\u0939\u091a\u093e\u0928:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0935\u0939 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<br>\n            (a) \u0906\u092f\u0924<br>(b) \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<br>(c) \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<br>(d) \u0935\u0930\u094d\u0917<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (b) \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<\/b>[cite: 29]<\/div>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 8: \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 10 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u0909\u0938\u0915\u0940 \u0926\u094b \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u0940?<br>\n            (a) 10 \u0938\u0947\u092e\u0940<br>(b) 20 \u0938\u0947\u092e\u0940<br>(c) 5 \u0938\u0947\u092e\u0940<br>(d) 2.5 \u0938\u0947\u092e\u0940<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (c) 5 \u0938\u0947\u092e\u0940<\/b>[cite: 33]<\/div>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 9: \u0938\u092e\u0924\u0932 \u0915\u0940 \u091f\u093e\u0907\u0932\u093f\u0902\u0917:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u0915\u094d\u092f\u093e \u0915\u093f\u0938\u0940 \u092d\u0940 \u0905\u0928\u093f\u092f\u092e\u093f\u0924 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c (4-gon) \u0938\u0947 \u0938\u092e\u0924\u0932 \u0915\u0940 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 (Tiling) \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948?<br>\n            (a) \u0928\u0939\u0940\u0902<br>(b) \u0939\u093e\u0901<br>(c) \u0915\u0947\u0935\u0932 \u0935\u0930\u094d\u0917 \u0915\u0947 \u0932\u093f\u090f \u0938\u0902\u092d\u0935 \u0939\u0948<br>(d) \u0907\u0928\u092e\u0947\u0902 \u0938\u0947 \u0915\u094b\u0908 \u0928\u0939\u0940\u0902<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (b) \u0939\u093e\u0901<\/b>[cite: 40]<\/div>\n        <\/div>\n        <div class=\"pargai-slide\">\n            <p><b>\u0938\u094d\u0932\u093e\u0907\u0921 10: \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0938\u0902\u092c\u0902\u0927:<\/b><\/p>\n            <div class=\"agniveer-box\">\u092a\u094d\u0930\u0936\u094d\u0928: \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0915\u093f\u0928\u094d\u0939\u0940\u0902 \u0926\u094b \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u093e \u0930\u0947\u0916\u093e\u0916\u0902\u0921 \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0938\u0947 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948?<br>\n            (a) \u0906\u0927\u093e \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930<br>(b) \u0926\u094b\u0917\u0941\u0928\u093e \u0914\u0930 \u0932\u0902\u092c\u0935\u0924<br>(c) \u092c\u0930\u093e\u092c\u0930 \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930<br>(d) \u0924\u093f\u0917\u0941\u0928\u093e<br>\n            <b>\u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: (a) \u0906\u0927\u093e \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930<\/b>[cite: 33]<\/div>\n        <\/div>\n    <\/div>\n\n    <div class=\"slider-footer-section\">\n        <button class=\"slider-nav-btn btn-prev\">\u092a\u093f\u091b\u0932\u093e (Prev)<\/button>\n        <span class=\"slider-page-counter\">1 \/ 10<\/span>\n        <button class=\"slider-nav-btn btn-next\">\u0905\u0917\u0932\u093e (Next)<\/button>\n    <\/div>\n<\/div><\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>\u092d\u093e\u0917 1: \u0905\u0927\u094d\u092f\u093e\u092f 12 &#8211; \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c (\u092a\u0930\u093f\u091a\u092f) \u0938\u094d\u0932\u093e\u0907\u0921 1: \u0905\u0927\u094d\u092f\u093e\u092f \u0915\u0940 \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e: \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c (\u092f\u093e 4-\u092d\u0941\u091c \/ 4-gon) \u0939\u092e\u093e\u0930\u0947 \u0926\u0948\u0928\u093f\u0915 \u091c\u0940\u0935\u0928 \u092e\u0947\u0902 \u0939\u0930 \u091c\u0917\u0939 \u092a\u093e\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902, \u091c\u0948\u0938\u0947 \u0935\u0930\u094d\u0917\u093e\u0915\u093e\u0930 \u091f\u093e\u0907\u0932\u094b\u0902 \u0938\u0947 \u092b\u0930\u094d\u0936 \u0915\u0940 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 (Tiling) \u0915\u0930\u0928\u093e[cite: 21]\u3002 \u0938\u094d\u0932\u093e\u0907\u0921 2: \u0938\u092e\u0924\u0932 \u0915\u0940 \u091f\u093e\u0907\u0932\u093f\u0902\u0917 (Tiling the Plane): \u0915\u093f\u0938\u0940 \u0938\u092e\u0924\u0932 \u0915\u094b \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u0905\u0902\u0924\u0930\u093e\u0932 (gaps) \u092f\u093e \u0905\u0924\u093f\u0935\u094d\u092f\u093e\u092a\u0928 (overlaps) \u0915\u0947 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