{"id":325,"date":"2022-04-13T10:41:42","date_gmt":"2022-04-13T10:41:42","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=325"},"modified":"2024-05-24T05:57:59","modified_gmt":"2024-05-24T05:57:59","slug":"q-3-pythagoras-inequality-theorems","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/q-3-pythagoras-inequality-theorems\/","title":{"rendered":"Q.3 Pythagoras&#8217; Inequality Theorems"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Pythagoras&#8217; Inequality Theorems<\/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\">If a, b, and c are the side lengths of a triangle and a\u2264b\u2264c, then:<br>a2+b2&gt;c2 if and only if the triangle is acute.<br>a2+b2=c2 if and only if the triangle is right.<br>a2+b2&lt;c2 if and only if the triangle is obtuse.<\/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-large-font-size\" style=\"background-color:#f1d2d2\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><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-5729293aac86c59962923b355ecdd4c9\" style=\"color:#b00012\"><strong>\ud83d\udcda The&nbsp;sides of a triangle have lengths&nbsp;6,&nbsp;8,&nbsp;and&nbsp;10.&nbsp;What kind of triangle is&nbsp;it?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>acute<\/li>\n\n\n\n<li>right<\/li>\n\n\n\n<li>obtuse<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First, put the three side lengths in order from smallest to largest: a=6, b=8, c=10.<\/li>\n\n\n\n<li>To classify the triangle, compare a<sup>2<\/sup>+b<sup>2<\/sup> to c<sup>2<\/sup>.<\/li>\n\n\n\n<li>a<sup>2<\/sup>+b<sup>2<\/sup> ? c<sup>2<\/sup><\/li>\n\n\n\n<li>6<sup>2<\/sup>+8<sup>2<\/sup> ? 10<sup>2<\/sup><\/li>\n\n\n\n<li>36+64 ? 100<\/li>\n\n\n\n<li>100 = 100<\/li>\n\n\n\n<li>Since 6<sup>2<\/sup>+8<sup>2<\/sup>=10<sup>2<\/sup>, these are the side lengths of a right triangle:<\/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=\"249\" height=\"291\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___300px___10_-removebg-preview.png\" alt=\"\" class=\"wp-image-4712\" style=\"width:304px;height:auto\"\/><\/figure><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d6f1e0\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><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-a731b14999d3784aef2d8b4b02cc8f22\" style=\"color:#b00012\"><strong>\ud83d\udcda The&nbsp;sides of a triangle have lengths&nbsp;3,&nbsp;4,&nbsp;and&nbsp;5.&nbsp;What kind of triangle is&nbsp;it?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>acute<\/li>\n\n\n\n<li>right<\/li>\n\n\n\n<li>obtuse<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First, put the three side lengths in order from smallest to largest: a=2, b=5, c=6.<\/li>\n\n\n\n<li>To classify the triangle, compare a<sup>2<\/sup>+b<sup>2<\/sup> to c<sup>2<\/sup>.<\/li>\n\n\n\n<li>a<sup>2<\/sup>+b<sup>2<\/sup> ? c<sup>2<\/sup><\/li>\n\n\n\n<li>22+52 ? 62<\/li>\n\n\n\n<li>4+25 ? 36<\/li>\n\n\n\n<li>29 &lt; 36<\/li>\n\n\n\n<li>Since 22+52&lt;62, these are the side lengths of an obtuse triangle:<\/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=\"253\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___300px___11_-removebg-preview.png\" alt=\"\" class=\"wp-image-4716\" style=\"width:341px;height:auto\"\/><\/figure><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#8096e769\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><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-59e2aff9acfcdaf0c330cb92951fa586\" style=\"color:#b00012\"><strong>\ud83d\udcda The&nbsp;sides of a triangle have lengths&nbsp;5,&nbsp;9,&nbsp;and&nbsp;9.&nbsp;What kind of triangle is&nbsp;it?<\/strong><\/p>\n\n\n\n<p>acute<\/p>\n\n\n\n<p>right<\/p>\n\n\n\n<p>obtuse<\/p>\n<\/div><\/div>\n\n\n\n<p>First, put the three side lengths in order from smallest to largest: a=5, b=9, c=9.<br>To classify the triangle, compare a<sup>2<\/sup>+b<sup>2<\/sup> to c2.<br>a<sup>2<\/sup>+b<sup>2<\/sup> ? c<sup>2<\/sup><br>5<sup>2<\/sup>+9<sup>2<\/sup> ? 9<sup>2<\/sup><br>25+81 ? 81<br>106 &gt; 81<br>Since 5<sup>2<\/sup>+9<sup>2<\/sup>&gt;9<sup>2<\/sup>, these are the side lengths of an acute triangle:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"396\" height=\"629\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-5.png\" alt=\"\" class=\"wp-image-4725\" style=\"aspect-ratio:0.6290909090909091;width:208px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-5.png 396w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-5-189x300.png 189w\" sizes=\"auto, (max-width: 396px) 100vw, 396px\" \/><\/figure><\/div><\/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\/73794\/828\/275\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-110.png\" alt=\"\" class=\"wp-image-7209\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-110.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-110-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-110-150x150.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\/38106\/821\/451\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-128.png\" alt=\"\" class=\"wp-image-7210\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-128.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-128-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-128-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Pythagoras&#8217; Inequality Theorems Key Notes : If a, b, and c are the side lengths of a triangle and a\u2264b\u2264c, then:a2+b2&gt;c2 if and only if the triangle is acute.a2+b2=c2 if and only if the triangle is right.a2+b2&lt;c2 if and only if the triangle is obtuse. Learn with an example \ud83d\udcda The&nbsp;sides of a triangle have<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/q-3-pythagoras-inequality-theorems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;Q.3 Pythagoras&#8217; Inequality Theorems&#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-325","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/325","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=325"}],"version-history":[{"count":9,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/325\/revisions"}],"predecessor-version":[{"id":12703,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/325\/revisions\/12703"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}