{"id":473,"date":"2022-04-13T11:05:01","date_gmt":"2022-04-13T11:05:01","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=473"},"modified":"2023-12-30T05:22:22","modified_gmt":"2023-12-30T05:22:22","slug":"aa-2-construct-an-equilateral-triangle-inscribed-in-a-circle","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/aa-2-construct-an-equilateral-triangle-inscribed-in-a-circle\/","title":{"rendered":"AA.2 Construct an equilateral triangle inscribed in a circle"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Construct an equilateral triangle inscribed in a circle<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-f79afd6ea8b322268468366b8e5f7cc7\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>An&nbsp;<strong>equilateral<\/strong><strong>&nbsp;<\/strong><strong>triangle<\/strong>&nbsp;has all three sides congruent and all angle measures equal to&nbsp;60\u00b0.<\/p>\n\n\n\n<p>Two&nbsp;chords in a circle are congruent if and only if their corresponding central angles are&nbsp;congruent.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#ecf6d2\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-0f271bbe0b739664ae001773e8ff557e\" style=\"color:#b00012\"><strong>The diagram below shows a nearly completed construction of an equilateral triangle inscribed in \u2a00A with a vertex at B. Complete the construction.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"716\" height=\"528\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.png\" alt=\"\" class=\"wp-image-11196\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.png 716w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2-300x221.png 300w\" sizes=\"auto, (max-width: 716px) 100vw, 716px\" \/><\/figure>\n\n\n\n<p>Part&nbsp;of the construction was done for you. Here are the steps to create this part of the&nbsp;construction.<\/p>\n\n\n\n<p><strong>Start<\/strong><strong>&nbsp;with the objects in the diagram&nbsp;<\/strong><strong>below.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"186\" height=\"195\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.1-removebg-preview.png\" alt=\"\" class=\"wp-image-11198\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the line through A and B.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"581\" height=\"337\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.2-removebg-preview.png\" alt=\"\" class=\"wp-image-11201\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.2-removebg-preview.png 581w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.2-removebg-preview-300x174.png 300w\" sizes=\"auto, (max-width: 581px) 100vw, 581px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"215\" height=\"307\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.3-removebg-preview.png\" alt=\"\" class=\"wp-image-11203\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.3-removebg-preview.png 215w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.3-removebg-preview-210x300.png 210w\" sizes=\"auto, (max-width: 215px) 100vw, 215px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a circle with radius AC centred at C.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"301\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.4-removebg-preview.png\" alt=\"\" class=\"wp-image-11208\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mark the points where \u2a00A and \u2a00C intersect. Call them D and E.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"268\" height=\"332\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.5-removebg-preview.png\" alt=\"\" class=\"wp-image-11210\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.5-removebg-preview.png 268w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.5-removebg-preview-242x300.png 242w\" sizes=\"auto, (max-width: 268px) 100vw, 268px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since C, D, and E are all on \u2a00A, AC=AD=AE. Since A, D, and E are all on \u2a00C, AC=CD=CE. This means that AC=AD=AE=CD=CE.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"297\" height=\"363\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.6-removebg-preview.png\" alt=\"\" class=\"wp-image-11232\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.6-removebg-preview.png 297w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.6-removebg-preview-245x300.png 245w\" sizes=\"auto, (max-width: 297px) 100vw, 297px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>So, \u25b3ACD and \u25b3ACE are congruent equilateral triangles.<\/li>\n\n\n\n<li>Draw the segment between B and D.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"255\" height=\"324\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.7-removebg-preview.png\" alt=\"\" class=\"wp-image-11233\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.7-removebg-preview.png 255w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.7-removebg-preview-236x300.png 236w\" sizes=\"auto, (max-width: 255px) 100vw, 255px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the segment between D and E.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"268\" height=\"319\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.8-removebg-preview.png\" alt=\"\" class=\"wp-image-11235\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.8-removebg-preview.png 268w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.8-removebg-preview-252x300.png 252w\" sizes=\"auto, (max-width: 268px) 100vw, 268px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Complete the construction.<\/strong><\/li>\n\n\n\n<li>To complete the construction of an equilateral triangle inscribed in \u2a00A with a vertex at B, carry out the following step:<\/li>\n\n\n\n<li>Draw the segment between B and E.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"268\" height=\"319\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.9-removebg-preview.png\" alt=\"\" class=\"wp-image-11239\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.9-removebg-preview.png 268w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.9-removebg-preview-252x300.png 252w\" sizes=\"auto, (max-width: 268px) 100vw, 268px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since \u25b3ACD and \u25b3ACE are both equilateral, m\u2220CAD and m\u2220CAE are both 60\u00b0. So, the supplementary angles \u2220BAD and \u2220BAE are both 120\u00b0.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"266\" height=\"346\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.10-removebg-preview.png\" alt=\"\" class=\"wp-image-11238\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.10-removebg-preview.png 266w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.10-removebg-preview-231x300.png 231w\" sizes=\"auto, (max-width: 266px) 100vw, 266px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Also, m\u2220DAE = m\u2220CAD + m\u2220CAE = 60\u00b0 + 60\u00b0 = 120\u00b0. Since the central angles \u2220BAD, \u2220BAE, and \u2220DAE are all congruent, so are the corresponding chords BD, BE, and DE.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"361\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.11-removebg-preview.png\" alt=\"\" class=\"wp-image-11240\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.11-removebg-preview.png 269w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/2.11-removebg-preview-224x300.png 224w\" sizes=\"auto, (max-width: 269px) 100vw, 269px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>So, \u25b3BDE is an equilateral triangle.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-d10c1106a03fa0d2c642217354ec023a\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/65576\/204\/172\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-175.png\" alt=\"\" class=\"wp-image-7532\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-175.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-175-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-175-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-194.png\" alt=\"\" class=\"wp-image-7533\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-194.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-194-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-194-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Construct an equilateral triangle inscribed in a circle Key Notes: An&nbsp;equilateral&nbsp;triangle&nbsp;has all three sides congruent and all angle measures equal to&nbsp;60\u00b0. Two&nbsp;chords in a circle are congruent if and only if their corresponding central angles are&nbsp;congruent. Learn with an example The diagram below shows a nearly completed construction of an equilateral triangle inscribed in \u2a00A<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/aa-2-construct-an-equilateral-triangle-inscribed-in-a-circle\/\">Continue reading <span class=\"screen-reader-text\">&#8220;AA.2 Construct an equilateral triangle inscribed in a circle&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-473","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/473","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=473"}],"version-history":[{"count":13,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/473\/revisions"}],"predecessor-version":[{"id":11243,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/473\/revisions\/11243"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=473"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}