{"id":405,"date":"2022-04-12T10:28:47","date_gmt":"2022-04-12T10:28:47","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=405"},"modified":"2024-10-23T15:49:44","modified_gmt":"2024-10-23T15:49:44","slug":"s-4-side-lengths-and-angle-measures-of-similar-figures","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/s-4-side-lengths-and-angle-measures-of-similar-figures\/","title":{"rendered":"S.4 Side lengths and angle measures of similar figures"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Side lengths and angle measures of similar figures<\/strong><\/h2>\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 class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">Key notes:<\/p>\n\n\n\n<p><strong>Similar Figures<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Similar figures are figures that have the same shape but not necessarily the same size.<\/li>\n\n\n\n<li>Two figures are similar if their corresponding angles are congruent and their corresponding sides are in proportion. &nbsp;<\/li>\n<\/ul>\n\n\n\n<p><strong>Scale Factor<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The scale factor is the ratio of the corresponding side lengths of two similar figures.<\/li>\n\n\n\n<li>If the scale factor is greater than 1, the second figure is larger than the first.<\/li>\n\n\n\n<li>If the scale factor is less than 1, the second figure is smaller than the first.<\/li>\n<\/ul>\n\n\n\n<p><strong>Properties of Similar Figures<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\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 ratio of the perimeters of two similar figures is equal to the scale factor.<\/li>\n\n\n\n<li>The ratio of the areas of two similar figures is equal to the square of the scale factor.<\/li>\n<\/ul>\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>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<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-43.png\" alt=\"\" class=\"wp-image-14588\" style=\"aspect-ratio:1.2376237623762376;width:394px;height:auto\"\/><\/figure><\/div>\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 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:#e0cbf8\"><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> If these two shapes are similar, what is the measure of the missing length&nbsp;<em>d<\/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=\"670\" height=\"300\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-3.png\" alt=\"\" class=\"wp-image-4965\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-3.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-3-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p><em>d<\/em>&nbsp;=&nbsp;______&nbsp;metres<\/p>\n<\/div><\/div>\n\n\n\n<p>Rotate the quadrilaterals to match up the corresponding parts.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__1_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-4966\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__1_-removebg-preview-2.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__1_-removebg-preview-2-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>The quadrilaterals&#8217; longer sides have a ratio of&nbsp; 4\/8 ,&nbsp;which is&nbsp;1\/2<\/p>\n\n\n\n<p>The quadrilaterals&#8217; shorter sides have a ratio of&nbsp; d\/2 ,<\/p>\n\n\n\n<p>Write a proportion:<\/p>\n\n\n\n<p>1\/2 = d\/2<\/p>\n\n\n\n<p>Multiply both sides by 2 \u00b7 2 and solve:<\/p>\n\n\n\n<p>2 = 2d<\/p>\n\n\n\n<p>2 \u00f7 2 = 2d \u00f7 2<\/p>\n\n\n\n<p>1 = d<\/p>\n\n\n\n<p>The missing length is 1 metre.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f8f6ce\"><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> If these two figures are similar, what is the measure of the missing angle?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-2-2.png\" alt=\"\" class=\"wp-image-4969\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-2-2.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-2-2-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>____\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Look at the angle with the question mark. Find the corresponding angle in the other shape.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__3_-removebg-preview.png\" alt=\"\" class=\"wp-image-4970\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__3_-removebg-preview.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__3_-removebg-preview-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>Since the shapes are similar, the measure of the missing angle is also 74\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f8d1d1\"><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>If these two figures are similar, what is the measure of the missing angle?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-4.png\" alt=\"\" class=\"wp-image-4971\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-4.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These-figures-are-congruent.-What-is-MO-kilometres-4-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>_____\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Look at the angle with the question mark. Find the corresponding angle in the other shape.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__5_-removebg-preview.png\" alt=\"\" class=\"wp-image-4972\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__5_-removebg-preview.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/These_figures_are_congruent._What_is_MO_kilometres__5_-removebg-preview-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>Since the shapes are similar, the measure of the missing angle is also 90\u00b0.<\/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<\/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\/80311\/759\/743\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-114.png\" alt=\"\" class=\"wp-image-6836\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-114.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-114-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-114-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-114-400x400.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\/80412\/480\/320\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-115.png\" alt=\"\" class=\"wp-image-6837\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-115.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-115-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-115-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-115-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Side lengths and angle measures of similar figures Key notes: Similar Figures Scale Factor Properties of Similar Figures Key Points to Remember: Learn with an example \ud83d\udd14 If these two shapes are similar, what is the measure of the missing length&nbsp;d? d&nbsp;=&nbsp;______&nbsp;metres Rotate the quadrilaterals to match up the corresponding parts. The quadrilaterals&#8217; longer sides<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/s-4-side-lengths-and-angle-measures-of-similar-figures\/\">Continue reading <span class=\"screen-reader-text\">&#8220;S.4 Side lengths and angle measures of similar figures&#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-405","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=\"Side lengths and angle measures of similar figures Key notes: Similar Figures Similar figures are figures that have the same shape but not necessarily the same size. 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