{"id":2909,"date":"2023-04-30T10:00:29","date_gmt":"2023-04-30T04:30:29","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=2909"},"modified":"2023-05-01T09:36:32","modified_gmt":"2023-05-01T04:06:32","slug":"find-angle-of-isosceles-triangle","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/find-angle-of-isosceles-triangle\/","title":{"rendered":"How Do You Find The Angle Of An Isosceles Triangle"},"content":{"rendered":"<h2><strong>How Do You Find The <a href=\"https:\/\/www.aplustopper.com\/what-is-angle-in-geometry\/\">Angle<\/a> Of An Isosceles <a href=\"https:\/\/www.aplustopper.com\/classification-of-triangles\/\">Triangle<\/a><\/strong><\/h2>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/V2iK77V-Q_g?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/3\/2878\/33509254663_1648945808_o.jpg\" alt=\"find-angle-of-isosceles-triangle-1\" width=\"681\" height=\"411\" \/><br \/>\n<strong>Theorem:<\/strong> Angles opposite to equal sides of an isosceles triangle are equal.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128504\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/How-Do-You-Find-The-Angle-Of-An-Isosceles-Triangle-1.png\" alt=\"How Do You Find The Angle Of An Isosceles Triangle 1\" width=\"343\" height=\"280\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/How-Do-You-Find-The-Angle-Of-An-Isosceles-Triangle-1.png 343w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/How-Do-You-Find-The-Angle-Of-An-Isosceles-Triangle-1-300x245.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><br \/>\n<strong>Given:<\/strong> In \u2206ABC, AB = AC<br \/>\n<strong>To Prove:<\/strong> \u2220B = \u2220C<br \/>\n<strong>Construction:<\/strong> Draw AD, bisector of \u2220A<br \/>\n\u2234 \u22201 = \u22202<br \/>\n<strong>Proof:<\/strong> In \u2206ADB &amp; \u2206ADC<br \/>\nAD = AD \u00a0 \u00a0 \u00a0(Common)<br \/>\n\u22201 = \u22202 \u00a0 \u00a0 \u00a0 \u00a0(by construction)<br \/>\nAB = AC<br \/>\nBy SAS, \u2206ADB \u2245 \u2206ADC<br \/>\n\u2234 \u2220B = \u2220C \u00a0 \u00a0 \u00a0 (c.p.c.t.) Proved.<\/p>\n<p><strong>Note:<\/strong> Other result: \u2220ADB = \u2220ADC \u00a0 \u00a0(c.p.c.t.)<br \/>\nBut \u2220ADB + \u2220ADC = 180\u00b0 \u00a0 \u00a0 \u00a0 \u00a0(linear pair)<br \/>\n\u2234 \u2220ADB = \u2220ADC = 90\u00b0 \u21d2 AD \u22a5 BC<br \/>\nand BD = DC (c.p.c.t.) \u21d2 AD is median<br \/>\n\u2234 we can say AD is perpendicular bisector of BC or we can say in isosceles \u2206, median is angle bisector and perpendicular to base also.<\/p>\n<p><b>Read More:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/angle-sum-property-of-triangle\/\"><span style=\"font-weight: 400;\">Angle Sum Property of a Triangle<\/span><\/a><\/li>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/median-altitude-of-triangle\/\"><span style=\"font-weight: 400;\">Median and Altitude of a Triangle<\/span><\/a><\/li>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/areas-of-two-similar-triangles\/\"><span style=\"font-weight: 400;\">Areas of Two Similar Triangles<\/span><\/a><\/li>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/area-of-a-triangle\/\"><span style=\"font-weight: 400;\">Area of A Triangle<\/span><\/a><\/li>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/congruent-triangles\/\"><span style=\"font-weight: 400;\">To Prove Triangles Are Congruent<\/span><\/a><\/li>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/similarity-of-triangles\/\"><span style=\"font-weight: 400;\">Criteria For Similarity of Triangles<\/span><\/a><\/li>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/construction-of-triangles-with-compass-and-protractor\/\"><span style=\"font-weight: 400;\">Construction of an Equilateral Triangle<\/span><\/a><\/li>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/classification-of-triangles\/\"><span style=\"font-weight: 400;\">Classification of Triangles<\/span><\/a><\/li>\n<\/ul>\n<h2><strong>Angle Of An Isosceles Triangle Example Problems With Solutions<\/strong><\/h2>\n<p><strong>Example 1: \u00a0 \u00a0<\/strong>Find \u2220BAC of an isosceles triangle in which AB = AC and \u2220B = 1\/3 of right angle.<br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/9\/8282\/29067707294_19e0841b5f_o.png\" alt=\"Angle-Of-An-Isosceles-Triangle-Example-1\" width=\"356\" height=\"122\" \/><\/p>\n<p><strong>Example 2: \u00a0 <\/strong>In isosceles triangle DEF, DE = EF and \u2220E = 70\u00b0 then find other two angles.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/9\/8509\/29693914945_8c57b915ff_o.png\" alt=\"Angle-Of-An-Isosceles-Triangle-Example-1\" width=\"220\" height=\"194\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/9\/8440\/29067707184_6d61daa67f_o.png\" alt=\"Angle-Of-An-Isosceles-Triangle-Example-2\" width=\"289\" height=\"210\" \/><\/p>\n<p><strong>Example 3: \u00a0 \u00a0<\/strong>\u2206ABC and \u2206DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see fig.). If AD is extended to intersect BC at P. Show that<br \/>\n(i) \u2206ABD \u2245\u00a0\u2206ACD<br \/>\n(ii) \u2206ABP \u2245\u00a0\u2206ACP<br \/>\n(iii) AP bisects \u2220A as well as \u2220D<br \/>\n(iv) AP is the perpendicular bisector of BC.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/9\/8589\/29067536564_54020b28a4_o.png\" alt=\"Angle-Of-An-Isosceles-Triangle-Example-2\" width=\"199\" height=\"205\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/9\/8150\/29069126503_2aae6ffd3f_o.png\" alt=\"Angle-Of-An-Isosceles-Triangle-Example-3\" width=\"383\" height=\"457\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/9\/8031\/29067707024_ea541fe812_o.png\" alt=\"Angle-Of-An-Isosceles-Triangle-Example-3-1\" width=\"383\" height=\"233\" \/><\/p>\n<p><strong>Example 4: \u00a0 \u00a0<\/strong>Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of \u2206PQR (see figure ). Show that:<br \/>\n(i) \u2206ABM \u2245 \u2206PQN \u00a0 \u00a0 \u00a0 \u00a0 (ii) \u2206ABC \u2245 \u2206PQR<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/9\/8368\/29693914805_71eef39562_o.png\" alt=\"Angle-Of-An-Isosceles-Triangle-Example-3\" width=\"419\" height=\"186\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/9\/8464\/29067706924_60fac601e7_o.png\" alt=\"Angle-Of-An-Isosceles-Triangle-Example-4\" width=\"355\" height=\"372\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>How Do You Find The Angle Of An Isosceles Triangle Theorem: Angles opposite to equal sides of an isosceles triangle are equal. Given: In \u2206ABC, AB = AC To Prove: \u2220B = \u2220C Construction: Draw AD, bisector of \u2220A \u2234 \u22201 = \u22202 Proof: In \u2206ADB &amp; \u2206ADC AD = AD \u00a0 \u00a0 \u00a0(Common) \u22201 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[1255,1257,1256,1254,71],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How Do You Find The Angle Of An Isosceles Triangle - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/find-angle-of-isosceles-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How Do You Find The Angle Of An Isosceles Triangle\" \/>\n<meta property=\"og:description\" content=\"How Do You Find The Angle Of An Isosceles Triangle Theorem: Angles opposite to equal sides of an isosceles triangle are equal. 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Given: In \u2206ABC, AB = AC To Prove: \u2220B = \u2220C Construction: Draw AD, bisector of \u2220A \u2234 \u22201 = \u22202 Proof: In \u2206ADB &amp; \u2206ADC AD = AD \u00a0 \u00a0 \u00a0(Common) \u22201 [&hellip;]","og_url":"https:\/\/www.aplustopper.com\/find-angle-of-isosceles-triangle\/","og_site_name":"A Plus Topper","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2023-04-30T04:30:29+00:00","article_modified_time":"2023-05-01T04:06:32+00:00","og_image":[{"url":"https:\/\/c1.staticflickr.com\/3\/2878\/33509254663_1648945808_o.jpg"}],"twitter_card":"summary","twitter_misc":{"Written by":"Veerendra","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/www.aplustopper.com\/#organization","name":"Aplus Topper","url":"https:\/\/www.aplustopper.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#logo","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/www.aplustopper.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/www.aplustopper.com\/#website","url":"https:\/\/www.aplustopper.com\/","name":"A Plus Topper","description":"Improve your Grades","publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.aplustopper.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/find-angle-of-isosceles-triangle\/#primaryimage","inLanguage":"en-US","url":"https:\/\/c1.staticflickr.com\/3\/2878\/33509254663_1648945808_o.jpg","contentUrl":"https:\/\/c1.staticflickr.com\/3\/2878\/33509254663_1648945808_o.jpg"},{"@type":"WebPage","@id":"https:\/\/www.aplustopper.com\/find-angle-of-isosceles-triangle\/#webpage","url":"https:\/\/www.aplustopper.com\/find-angle-of-isosceles-triangle\/","name":"How Do You Find The Angle Of An Isosceles Triangle - 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