{"id":407,"date":"2022-04-12T10:29:08","date_gmt":"2022-04-12T10:29:08","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=407"},"modified":"2024-10-23T15:55:54","modified_gmt":"2024-10-23T15:55:54","slug":"s-5-similar-figures-and-indirect-measurement","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/s-5-similar-figures-and-indirect-measurement\/","title":{"rendered":"S.5 Similar figures and indirect measurement"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Similar figures and indirect measurement<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">Key notes:<\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Similar Figures<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Similar figures have the same shape but not necessarily the same size.<\/li>\n\n\n\n<li>Corresponding angles of similar figures are congruent.<\/li>\n\n\n\n<li>Corresponding sides of similar figures are in proportion. &nbsp;<\/li>\n\n\n\n<li>The scale factor is the ratio of the corresponding side lengths of two similar figures.<\/li>\n<\/ul>\n\n\n\n<p><strong>Indirect Measurement<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Indirect measurement is a technique used to find the length or height of an object without directly measuring it.<\/li>\n\n\n\n<li>It often involves using similar triangles.<\/li>\n<\/ul>\n\n\n\n<p><strong>Steps for Indirect Measurement Using Similar Triangles:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify similar triangles:<\/strong> Look for two triangles that have the same shape and corresponding angles.<\/li>\n\n\n\n<li><strong>Set up a proportion:<\/strong> Write a proportion using the corresponding side lengths of the similar triangles.<\/li>\n\n\n\n<li><strong>Solve for the missing measurement:<\/strong> Use cross-multiplication or other algebraic methods to solve for the missing measurement.<\/li>\n<\/ol>\n\n\n\n<p><strong>Key Points to Remember:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Similar figures have the same shape but not necessarily the same size.<\/li>\n\n\n\n<li>Indirect measurement uses similar triangles to find unknown measurements.<\/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=\"250\" height=\"202\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-44.png\" alt=\"\" class=\"wp-image-14592\" style=\"aspect-ratio:1.2376237623762376;width:376px;height:auto\"\/><\/figure><\/div>\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\" style=\"background-color:#dbe5ff\"><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\" style=\"color:#b00012\">\ud83d\udd14<strong> In the diagram below, \u2206CDE \u2206FGE. Find w.<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px.png\" alt=\"\" class=\"wp-image-4975\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Write your answer as a whole number or a decimal. Do not round.<\/p>\n\n\n\n<p>w =____ metres<\/p>\n<\/div><\/div>\n\n\n\n<p>The original diagram included a smaller triangle and a larger triangle. Redraw them as separate triangles with corresponding sides in the same colour.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview.png\" alt=\"\" class=\"wp-image-4976\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>\u2206CDE ~ \u2206FGE means that \u2206CDE is similar to \u2206FGE.<\/p>\n\n\n\n<p>One pair of corresponding side lengths is FG and CD. Together they form the fraction FG\/CD ,<\/p>\n\n\n\n<p>Another pair of corresponding side lengths is EF and EC. Together they form the fraction EF\/EC<\/p>\n\n\n\n<p>In both fractions, the numerator comes from \u2206FGE and the denominator comes from \u2206CDE. Since the triangles are similar, you can use the fractions to set up a proportion and solve for w.<\/p>\n\n\n\n<p>FG\/CD = EF\/EC<\/p>\n\n\n\n<p>6\/3 = 10\/W                                           Plug in the side lengths<\/p>\n\n\n\n<p>6\/3 (3W) = 10\/W (3W)                     Multiply both sides by 3w<\/p>\n\n\n\n<p>6 w=10 \u00b7 3                                    Simplify<\/p>\n\n\n\n<p>6W = 30                                  <em>Simplify<\/em> <\/p>\n\n\n\n<p>6 w \u00f7 6 = 30 \u00f7 6                Divide both sides by 6<\/p>\n\n\n\n<p>W = 5<\/p>\n\n\n\n<p>The missing length is 5 metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#d9f8db\"><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\" style=\"color:#b00012\">\ud83d\udd14<strong> In the diagram below, RQP RON. Find q.<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-1.png\" alt=\"\" class=\"wp-image-4981\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-1.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-1-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-1-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-1-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p><em>Write your answer as a whole number or a decimal. Do not round.<\/em><\/p>\n\n\n\n<p>q = ____ metres<\/p>\n<\/div><\/div>\n\n\n\n<p>The original diagram included a smaller triangle and a larger triangle. Redraw them as separate triangles with corresponding sides in the same colour.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-4983\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview-1.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview-1-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview-1-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___1_-removebg-preview-1-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>\u2206RQP \u2206RON means that \u2206RQP is similar to \u2206RON.<\/p>\n\n\n\n<p>One pair of corresponding side lengths is PR and NR. Together they form the fraction PR\/NR ,<\/p>\n\n\n\n<p>Another pair of corresponding side lengths is RQ and RO. Together they form the fraction RQ\/RO<\/p>\n\n\n\n<p>In both fractions, the numerator comes from RQP and the denominator comes from RON. Since the triangles are similar, you can use the fractions to set up a proportion and solve for q.<\/p>\n\n\n\n<p>PR\/NR = RQ\/RO<\/p>\n\n\n\n<p>5\/10 = 4\/q                                       Plug in the side lengths<\/p>\n\n\n\n<p>5\/10 (10q) = 4\/q (10q)                Multiply both sides by 10q<\/p>\n\n\n\n<p>5 q = 4 \u00b7 10                             Simplify<\/p>\n\n\n\n<p>5q = 40                              Simplify<\/p>\n\n\n\n<p>5 q \u00f7 5 = 40 \u00f7 5           Divide both sides by 5<\/p>\n\n\n\n<p>q = 8<\/p>\n\n\n\n<p>The missing length is 8 metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#fdddfa\"><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\" style=\"color:#b00012\">\ud83d\udd14 <strong>Find&nbsp;<em>g<\/em>.<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-2-1.png\" alt=\"\" class=\"wp-image-4984\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-2-1.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-2-1-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-2-1-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-670-\u00d7-100px-500-\u00d7-500px-2-1-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Write your answer as a whole number or a decimal. Do not round.<\/p>\n\n\n\n<p>g = _____ metres<\/p>\n<\/div><\/div>\n\n\n\n<p>The original diagram included a smaller triangle inside a larger triangle. Redraw them as separate triangles.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___3_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-4985\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___3_-removebg-preview-1.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___3_-removebg-preview-1-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___3_-removebg-preview-1-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__670___100px___500___500px___3_-removebg-preview-1-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>\u2206GHI is similar to \u2206KHJ because all three pairs of corresponding angles are congruent.<\/p>\n\n\n\n<p>One pair of corresponding side lengths is KH and GH. Together they form the fraction KH\/GH ,<\/p>\n\n\n\n<p>Another pair of corresponding side lengths is JK and IG. Together they form the fraction JK\/IG .<\/p>\n\n\n\n<p>In both fractions, the numerator comes from \u2206KHJ and the denominator comes from \u2206GHI. Since the triangles are similar, you can use the fractions to set up a proportion and solve for g.<\/p>\n\n\n\n<p>KH\/GH = JK\/IG<\/p>\n\n\n\n<p>8\/4 = 6\/g                                  Plug in the side lengths<\/p>\n\n\n\n<p>8\/4 (4g) = 6\/g (4g)               Multiply both sides by 4g<\/p>\n\n\n\n<p>8g = 6.4                            Simplify<\/p>\n\n\n\n<p>8g = 24                         Simplify<\/p>\n\n\n\n<p>8 g \u00f7 8 = 24 \u00f7 8      Divide both sides by 8<\/p>\n\n\n\n<p>g = 3<\/p>\n\n\n\n<p>The missing length is 3 metres.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n<\/div><\/div>\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\/80320\/518\/226\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-115.png\" alt=\"\" class=\"wp-image-6839\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-115.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-115-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-115-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-115-400x400.png 400w\" 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\/80472\/026\/468\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-116.png\" alt=\"\" class=\"wp-image-6840\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-116.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-116-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-116-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-116-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Similar figures and indirect measurement Key notes: Similar Figures Indirect Measurement Steps for Indirect Measurement Using Similar Triangles: Key Points to Remember: Learn with an example \ud83d\udd14 In the diagram below, \u2206CDE \u2206FGE. Find w. Write your answer as a whole number or a decimal. Do not round. w =____ metres The original diagram included<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/s-5-similar-figures-and-indirect-measurement\/\">Continue reading <span class=\"screen-reader-text\">&#8220;S.5 Similar figures and indirect measurement&#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,"footnotes":""},"class_list":["post-407","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"Similar figures and indirect measurement Key notes: Similar Figures Similar figures have the same shape but not necessarily the same size. Corresponding angles of similar figures are congruent. 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Corresponding angles of similar figures are congruent. Corresponding sides of similar figures are in proportion. The scale factor is the ratio of the corresponding side lengths of two similar figures. 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