{"id":112,"date":"2022-04-13T08:22:23","date_gmt":"2022-04-13T08:22:23","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=112"},"modified":"2025-10-31T09:11:10","modified_gmt":"2025-10-31T09:11:10","slug":"g-6-triangle-inequality-theorem","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/g-6-triangle-inequality-theorem\/","title":{"rendered":"G.6 Triangle Inequality Theorem"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Triangle Inequality Theorem<\/strong><\/h2>\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\" style=\"flex-basis:100%\">\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\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAG3WDjR4r0\/19pIax995zHJ5fDfl0yktA\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3WDjR4r0&#x2F;19pIax995zHJ5fDfl0yktA&#x2F;watch?utm_content=DAG3WDjR4r0&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Design<\/a> by Delta publications\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b;text-transform:capitalize\"><strong>key notes :<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe2 <strong>Triangle Inequality Theorem<\/strong><\/h3>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-18980f4e2d071bd50dcb4dd9c8d7678b\" style=\"color:#000060\">\ud83d\udd3a <strong>Definition:<\/strong><\/p>\n\n\n\n<p>The sum of the lengths of <strong>any two sides of a triangle<\/strong> is <strong>always greater than<\/strong> the length of the third side. <strong>Formula:<\/strong><br>If a triangle has sides <strong>a, b, c<\/strong>, then:<\/p>\n\n\n\n<p>a + b &gt; c<\/p>\n\n\n\n<p>b + c &gt; a<\/p>\n\n\n\n<p>a + c &gt; b<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-671fef6b99342c4a2c5e074559894c0f\" style=\"color:#000060\">\ud83d\udd39 <strong>Purpose:<\/strong><\/p>\n\n\n\n<p>Helps to <strong>check whether three given lengths can form a triangle<\/strong>.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-f9cf604c666a1e17da2edefec49dadfb\" style=\"color:#000060\">\ud83d\udd39 <strong>Example:<\/strong><\/p>\n\n\n\n<p>If sides are <strong>3 cm, 4 cm, 8 cm<\/strong> \u2192 Can they form a triangle?<\/p>\n\n\n\n<p>3 + 4 = 7 \u274c (not &gt; 8)<\/p>\n\n\n\n<p>\u2705 <strong>So, no triangle is possible.<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-47187cdd5776bbfad2e98b6a6499a618\" style=\"color:#000060\">\ud83d\udd39 <strong>Important Points:<\/strong><\/p>\n\n\n\n<p>\u26a0\ufe0f The sum of <strong>two sides must be strictly greater<\/strong>, not equal.<\/p>\n\n\n\n<p>\u2705 Always check <strong>all three combinations<\/strong>.<\/p>\n\n\n\n<p>\ud83d\udd04 Works for <strong>all types of triangles<\/strong>: scalene, isosceles, equilateral.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-95d070466a5fc73c772231014287760c\" style=\"color:#000060\">\ud83c\udf1f <strong>Mnemonic Tip:<\/strong><\/p>\n\n\n\n<p>\u201c<strong>Any two sides together must be bigger than the third side<\/strong>\u201d \ud83d\udc6b\u2795\ud83d\udc6b &gt; \ud83d\udc6c<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e366cf2ee9f07734149ba8849b0e8d03\" style=\"color:#000060\">\ud83d\udd8c\ufe0f <strong>Visual Representation:<\/strong><\/p>\n\n\n\n<p>Draw a triangle and label sides a, b, c.<\/p>\n\n\n\n<p>Show arrows with a + b &gt; c, etc. to <strong>remember the theorem easily<\/strong>.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-f005b96eda723a2e3506c4d9d0c4b862\" style=\"color:#000060\">\ud83d\udca1 <strong>Real-life Example:<\/strong><\/p>\n\n\n\n<p>Building a <strong>triangular roof<\/strong> \ud83c\udfe0<\/p>\n\n\n\n<p>Connecting <strong>supports in a triangular frame<\/strong> \ud83c\udfd7\ufe0f<\/p>\n\n\n\n<p>Ensures <strong>structure is stable<\/strong> and possible.<\/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<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#afd9ee\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background\" style=\"color:#b00012\"><strong>Can&nbsp;the sides of a triangle have lengths&nbsp;1,&nbsp;6,&nbsp;and&nbsp;9?<\/strong><\/p>\n\n\n\n<p>First,&nbsp;put the three numbers in order from smallest to largest:&nbsp;a=1,&nbsp;b=6,&nbsp;and&nbsp;c=9. <\/p>\n\n\n\n<p>Now&nbsp;check whether&nbsp;a+b&gt;c.&nbsp;Since&nbsp;1+6=7,&nbsp;it is false that&nbsp;1+6&gt;9.&nbsp;So, these are not the side lengths of a&nbsp;triangle.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f4bee9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background\" style=\"color:#b00012\"><strong>Can&nbsp;the sides of a triangle have lengths&nbsp;1,&nbsp;2,&nbsp;and&nbsp;3?<\/strong><\/p>\n\n\n\n<p>First,&nbsp;put the three numbers in order from smallest to largest:&nbsp;a=1,&nbsp;b=2,&nbsp;and&nbsp;c=3.<\/p>\n\n\n\n<p>Now&nbsp;check whether&nbsp;a+b&gt;c.&nbsp;Since&nbsp;1+2=3,&nbsp;it is false that&nbsp;1+2&gt;3.&nbsp;So, these are not the side lengths of a&nbsp;triangle.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#e9f6a1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background\" style=\"color:#b00012\"><strong>Can&nbsp;the sides of a triangle have lengths&nbsp;3,&nbsp;6,&nbsp;and&nbsp;8?<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\">First,&nbsp;put the three numbers in order from smallest to largest:&nbsp;a=3,&nbsp;b=6,&nbsp;and&nbsp;c=8.<\/p>\n\n\n\n<p>Now&nbsp;check whether&nbsp;a+b&gt;c.&nbsp;Since&nbsp;3+6=9,&nbsp;it is true that&nbsp;3+6&gt;8.&nbsp;So, these are the side lengths of a&nbsp;triangle.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#b4faba\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background\" style=\"color:#b00012\"><strong>Can&nbsp;the sides of a triangle have lengths&nbsp;3,&nbsp;6,&nbsp;and&nbsp;10?<\/strong><\/p>\n\n\n\n<p>First,&nbsp;put the three numbers in order from smallest to largest:&nbsp;a=3,&nbsp;b=6,&nbsp;and&nbsp;c=10.<\/p>\n\n\n\n<p>Now&nbsp;check whether&nbsp;a+b&gt;c.&nbsp;Since&nbsp;3+6=9,&nbsp;it is false that&nbsp;3+6&gt;10.&nbsp;So, these are not the side lengths of a&nbsp;triangle.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#ecc0fa\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background\" style=\"color:#b00012\"><strong>Can&nbsp;the sides of a triangle have lengths&nbsp;2,&nbsp;3,&nbsp;and&nbsp;5?<\/strong><\/p>\n\n\n\n<p>First,&nbsp;put the three numbers in order from smallest to largest:&nbsp;a=2,&nbsp;b=3,&nbsp;and&nbsp;c=5.<\/p>\n\n\n\n<p>Now&nbsp;check whether&nbsp;a+b&gt;c.&nbsp;Since&nbsp;2+3=5,&nbsp;it is false that&nbsp;2+3&gt;5.&nbsp;So, these are not the side lengths of a&nbsp;triangle.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#cfe8fa\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background\" style=\"color:#b00012\"><strong>Can&nbsp;the sides of a triangle have lengths&nbsp;2,&nbsp;7,&nbsp;and&nbsp;10?<\/strong><\/p>\n\n\n\n<p>First,&nbsp;put the three numbers in order from smallest to largest:&nbsp;a=2,&nbsp;b=7,&nbsp;and&nbsp;c=10.<\/p>\n\n\n\n<p>Now&nbsp;check whether&nbsp;a+b&gt;c.&nbsp;Since&nbsp;2+7=9,&nbsp;it is false that&nbsp;2+7&gt;10.&nbsp;So, these are not the side lengths of a&nbsp;triangle.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f9cfc1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background\" style=\"color:#b00012\"><strong>Can&nbsp;the sides of a triangle have lengths&nbsp;1,&nbsp;10,&nbsp;and&nbsp;10?<\/strong><\/p>\n\n\n\n<p>First,&nbsp;put the three numbers in order from smallest to largest:&nbsp;a=1,&nbsp;b=10,&nbsp;and&nbsp;c=10.<\/p>\n\n\n\n<p>Now&nbsp;check whether&nbsp;a+b&gt;c.&nbsp;Since&nbsp;1+10=11,&nbsp;it is true that&nbsp;1+10&gt;10.&nbsp;So, these are the side lengths of a&nbsp;triangle.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns are-vertically-aligned-center has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#ffef76\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-7.png\" alt=\"\" class=\"wp-image-10117\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-7.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-7-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-7-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/16957199278084hk286wc-voicemaker.in-speech.mp3\"><\/audio><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!<\/strong><\/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\/81351\/948\/938\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34.png\" alt=\"\" class=\"wp-image-7757\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34-150x150.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\/81097\/390\/943\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-37.png\" alt=\"\" class=\"wp-image-7758\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-37.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-37-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-37-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Triangle Inequality Theorem Design by Delta publications key notes : \ud83d\udfe2 Triangle Inequality Theorem \ud83d\udd3a Definition: The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. Formula:If a triangle has sides a, b, c, then: a + b &gt; c b + c<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/g-6-triangle-inequality-theorem\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.6 Triangle Inequality Theorem&#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-112","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/112","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=112"}],"version-history":[{"count":30,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/112\/revisions"}],"predecessor-version":[{"id":18159,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/112\/revisions\/18159"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}