{"id":291,"date":"2022-04-13T10:34:55","date_gmt":"2022-04-13T10:34:55","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=291"},"modified":"2024-10-22T11:33:45","modified_gmt":"2024-10-22T11:33:45","slug":"o-4-triangles-and-bisectors","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/o-4-triangles-and-bisectors\/","title":{"rendered":"O.4 Triangles and bisectors"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Triangles and bisectors<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-large-font-size\">\ud83d\udcda A point is equidistant from two lines if it is the same distance from them. The distance between a point and a line is the length of the segment perpendicular to the line from the point.<br>\ud83d\udcda The <strong>Angle Bisector Theorem<\/strong> states that a point is on the bisector of an angle if and only if it is in the interior of the angle and is equidistant from the sides of the angle.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"483\" height=\"382\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-49.png\" alt=\"\" class=\"wp-image-11366\" style=\"width:316px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-49.png 483w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-49-300x237.png 300w\" sizes=\"auto, (max-width: 483px) 100vw, 483px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\">D&nbsp;is on the angle bisector of&nbsp;\u2220ABC&nbsp;if and only if it is in the interior of&nbsp;\u2220ABC&nbsp;and&nbsp;AD\u2245CD.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<br><\/strong><\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#efcbcb\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-f0aac94d3f71b83c1b037b703593b982\" style=\"color:#b00012\"><strong>\u2708\ufe0f What&nbsp;is&nbsp;<em>TU<\/em>?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-41.png\" alt=\"\" class=\"wp-image-11367\" style=\"aspect-ratio:0.9393939393939394;width:302px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-41.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-41-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-41-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>TU = _______<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Look&nbsp;at the&nbsp;diagram.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T134443.624.png\" alt=\"\" class=\"wp-image-11368\" style=\"width:368px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T134443.624.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T134443.624-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T134443.624-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Since&nbsp;\u2220RSU \u2245 \u2220TSU, SU bisects&nbsp;\u2220RST.<\/p>\n\n\n\n<p>Therefore,&nbsp;RU \u2245 TU by the Angle Bisector&nbsp;Theorem.<\/p>\n\n\n\n<p>So,&nbsp;TU = RU = 45.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f2c5f2\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-c70f102b7fc2aaba95ebc1bb684aa46a\" style=\"color:#b00012\"><strong>\u2708\ufe0f What&nbsp;is&nbsp;<em>DE<\/em>? <\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-42.png\" alt=\"\" class=\"wp-image-11370\" style=\"width:343px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-42.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-42-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-42-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>DE = ______<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Look&nbsp;at the&nbsp;diagram.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"220\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T133615.878.png\" alt=\"\" class=\"wp-image-11365\" style=\"aspect-ratio:0.7328042328042328;width:293px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Since&nbsp;\u2220DFE&nbsp;is a right angle and&nbsp;<em>CF<\/em>=<em>EF<\/em>=58,&nbsp;DF&nbsp;is the perpendicular bisector of&nbsp;CE. <\/li>\n\n\n\n<li>Therefore,&nbsp;CD \u2245 DE&nbsp;by the Perpendicular Bisector&nbsp;Theorem.<\/li>\n\n\n\n<li>So,&nbsp;<em>DE<\/em>=<em>CD<\/em>=70.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f1b8c6\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-a94d72e7622a13580a8b7b96443345ec\" style=\"color:#b00012\"><strong>If RS \u2245 ST and TU = 58, What is RT ?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-43.png\" alt=\"\" class=\"wp-image-11374\" style=\"width:252px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-43.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-43-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-43-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>RT = ________<\/p>\n<\/div><\/div>\n\n\n\n<p>Label the diagram with the information given in the question.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__44_-removebg-preview.png\" alt=\"\" class=\"wp-image-11376\" style=\"width:358px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__44_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__44_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__44_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Since&nbsp; RS \u2245 ST ,S&nbsp;is equidistant from the endpoints of&nbsp;RT.&nbsp;Therefore,&nbsp;S&nbsp;lies on the perpendicular bisector of&nbsp;RT&nbsp;by the Perpendicular Bisector&nbsp;Theorem.<\/p>\n\n\n\n<p>Since&nbsp;S&nbsp;is on the perpendicular bisector of&nbsp;RT&nbsp;and&nbsp;\u2220SUT&nbsp;is a right angle,&nbsp;SU&nbsp;is the perpendicular bisector of&nbsp;RT.<\/p>\n\n\n\n<p>So,&nbsp;RU = TU = 58&nbsp;and&nbsp;RT = 2 .58 = 116.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!<\/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\/80411\/145\/932\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-95.png\" alt=\"\" class=\"wp-image-7141\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-95.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-95-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-95-150x150.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\"><a href=\"https:\/\/wordwall.net\/play\/80178\/701\/474\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-113.png\" alt=\"\" class=\"wp-image-7142\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-113.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-113-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-113-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Triangles and bisectors Key Notes : \ud83d\udcda A point is equidistant from two lines if it is the same distance from them. The distance between a point and a line is the length of the segment perpendicular to the line from the point.\ud83d\udcda The Angle Bisector Theorem states that a point is on the bisector<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/o-4-triangles-and-bisectors\/\">Continue reading <span class=\"screen-reader-text\">&#8220;O.4 Triangles and bisectors&#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-291","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/291","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=291"}],"version-history":[{"count":11,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/291\/revisions"}],"predecessor-version":[{"id":14228,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/291\/revisions\/14228"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}