{"id":7772,"date":"2023-03-27T12:10:00","date_gmt":"2023-03-27T06:40:00","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=7772"},"modified":"2023-03-25T13:13:20","modified_gmt":"2023-03-25T07:43:20","slug":"similar-triangles-formula","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/similar-triangles-formula\/","title":{"rendered":"Similar Triangles Formula"},"content":{"rendered":"\n<p>Similar triangles is quite a useful topics for Geometry. It is quite widely used in Physics  also. Here are Similar Triangles Formula to help you dela with variety of problems<\/p>\n\n\n\n<p><strong>Formula  1<\/strong><\/p>\n\n\n\n<p>If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"263\" height=\"223\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-1.png\" alt=\"Similar Triangles Formula\" class=\"wp-image-7773\"\/><\/a><\/figure>\n\n\n\n<p>$\\frac {AD}{AB} = \\frac {AE}{AC}$<\/p>\n\n\n\n<p><strong>Formula 2<\/strong><\/p>\n\n\n\n<p>If sides are in Proportion, the lines DE || BC<\/p>\n\n\n\n<p><strong>Formula 3<\/strong><\/p>\n\n\n\n<p>Side and Angles For Similar Triangles<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-2.png\"><img loading=\"lazy\" decoding=\"async\" width=\"527\" height=\"221\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-2.png\" alt=\"\" class=\"wp-image-7774\" srcset=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-2.png 527w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-2-300x126.png 300w\" sizes=\"auto, (max-width: 527px) 100vw, 527px\" \/><\/a><\/figure>\n\n\n\n<p>$\\Delta ABC \\sim \\Delta DEF$<\/p>\n\n\n\n<p>$\\angle A = \\angle D$, $\\angle B = \\angle E $, $\\angle C = \\angle F$<br>$\\frac {AB}{DE}=\\frac {AC}{DF} =\\frac {BC}{EF}$<\/p>\n\n\n\n<p><strong>Formula 4<\/strong><\/p>\n\n\n\n<p>Perimeter for Similar Triangles<\/p>\n\n\n\n<p>$\\frac {AB}{DE}=\\frac {AC}{DF} =\\frac {BC}{EF} = \\frac {\\text{perimeter of triangle ABC}}{\\text {perimeter of triangle DEF}}$<\/p>\n\n\n\n<p><strong>Formula 5<\/strong><\/p>\n\n\n\n<p>Area for Similar Triangles<\/p>\n\n\n\n<p>$\\frac {\\text {Area of triangle ABC}}{\\text{Area of triangle DEF}}= \\frac {AB^2}{DE^2}=\\frac {AC^2}{DF^2} =\\frac {BC^2}{EF^2} $<\/p>\n\n\n\n<p><strong>Formula 6<\/strong><\/p>\n\n\n\n<p>AAA Similarity  Criterion<\/p>\n\n\n\n<p>If the three angles  are equal to the corresponding angles of other triangles , then the triangles are Similar<\/p>\n\n\n\n<p>If $\\angle A = \\angle D$, $\\angle B = \\angle E $, $\\angle C = \\angle F$<br>then $\\Delta ABC \\sim \\Delta DEF$ and <br>$\\frac {AB}{DE}=\\frac {AC}{DF} =\\frac {BC}{EF}$<\/p>\n\n\n\n<p><strong>Formula 7<\/strong><\/p>\n\n\n\n<p>AA Similarity  Criterion<\/p>\n\n\n\n<p>It is same as above . if two angles are same, the third angle will always be same<\/p>\n\n\n\n<p>If $\\angle A = \\angle D$, $\\angle B = \\angle E $ <br>then  $\\angle C= \\angle F $  , $\\Delta ABC \\sim \\Delta DEF$ and <br>$\\frac {AB}{DE}=\\frac {AC}{DF} =\\frac {BC}{EF}$<\/p>\n\n\n\n<p><strong>Formula 8<\/strong><\/p>\n\n\n\n<p>SSS Similarity Criterion<\/p>\n\n\n\n<p>If the sides of the two triangles are in same proportion, then triangles are similar<\/p>\n\n\n\n<p>$\\frac {AB}{DE}=\\frac {AC}{DF} =\\frac {BC}{EF}$<br>then $\\Delta ABC \\sim \\Delta DEF$<br>and  $\\angle A = \\angle D$, $\\angle B = \\angle E $,$\\angle C= \\angle F $ <\/p>\n\n\n\n<p><strong>Formula 9<\/strong><\/p>\n\n\n\n<p>SAS Similarity Criterion<\/p>\n\n\n\n<p>if the one angle of a triangle is equal to one angle of other triangles and sides including that angle is \u00a0proportional, then the triangles are similar<\/p>\n\n\n\n<p>$\\frac {AB}{DE}=\\frac {AC}{DF} $ and $\\angle A = \\angle D$<br>then $\\Delta ABC \\sim \\Delta DEF$<br>and  $\\angle B = \\angle E $,$\\angle C= \\angle F $ <br>and $\\frac {AB}{DE}=\\frac {AC}{DF} =\\frac {BC}{EF}$<\/p>\n\n\n\n<p><strong>Formula 10<\/strong><\/p>\n\n\n\n<p>Pythagoras Theorem<\/p>\n\n\n\n<p>In a right angle triangle<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-3.png\"><img loading=\"lazy\" decoding=\"async\" width=\"190\" height=\"174\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-3.png\" alt=\"\" class=\"wp-image-7775\"\/><\/a><\/figure>\n\n\n\n<p>$AC^2 = AB^2 + BC^2$<br>AC is called the hypotenuse<br>BC is called the base<br>AB is the height<\/p>\n\n\n\n<p><strong>Formula 11<\/strong><\/p>\n\n\n\n<p>RHS Similarity Criterion<\/p>\n\n\n\n<p>If in two right triangles, hypotenuse and one side of one triangle are proportional to the hypotenuse and one side of the other triangle,<br>then the two triangles are similar<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-4.png\"><img loading=\"lazy\" decoding=\"async\" width=\"362\" height=\"182\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-4.png\" alt=\"\" class=\"wp-image-7776\" srcset=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-4.png 362w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/03\/similar-triangles-formula-4-300x151.png 300w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><\/a><\/figure>\n\n\n\n<p>If $\\frac {AB}{DE}= \\frac {AC}{DF}$ and $\\angle B = \\angle E= 90^0$<br>then $\\Delta ABC \\sim \\Delta DEF$<br>and $\\frac {AB}{DE}= \\frac {AC}{DF} = \\frac {BC}{EF}<br>and $\\angle A = \\angle D$ and $\\angle C = \\angle F$<\/p>\n\n\n\n<p>I hope you will find these formula useful<\/p>\n\n\n\n<p><strong>Related Articles<\/strong><br><a href=\"https:\/\/physicscatalyst.com\/Class10\/similar_triangles.php\">Similar Triangles Class 10 Notes<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Similar triangles is quite a useful topics for Geometry. It is quite widely used in Physics also. Here are Similar Triangles Formula to help you dela with variety of problems Formula 1 If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the [&hellip;]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[498],"tags":[],"class_list":["post-7772","post","type-post","status-publish","format-standard","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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Here are Similar Triangles Formula to help you dela with variety of problems Formula 1 If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the&hellip;","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7772","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=7772"}],"version-history":[{"count":1,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7772\/revisions"}],"predecessor-version":[{"id":7777,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7772\/revisions\/7777"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=7772"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=7772"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=7772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}