{"id":3643,"date":"2022-02-06T12:06:02","date_gmt":"2022-02-06T12:06:02","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=3643"},"modified":"2022-03-04T13:55:30","modified_gmt":"2022-03-04T13:55:30","slug":"similarity-statement","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/similarity-statement\/","title":{"rendered":"Similarity Statement"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Similarity Statement<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Similarity is an important concept in geometry that helps prove some theorems and their corollaries. The statement of similarity is based on the fact that for two shapes to be similar, they have to have the same angles and their sides have to be in proportion.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. Take the corresponding sides of the polygons and set up ratios.<br \/>\n2. If all the ratios are same, the polygons are similar. When two polygons are similar, then their corresponding angles are congruent and the measures of their corresponding sides are proportional. The similarity statement can be found.<br \/>\n3. If all the ratios are not same, the polygons are not similar. The similarity statement cannot be found.<br \/>\n4. To determine the <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations\">similarity statement<\/a>, place the corresponding angles in order for both polygons.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">Write the similarity statement for the figures below.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations\"><img loading=\"lazy\" class=\"alignnone wp-image-3645 \" style=\"margin-top: 10px;\" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1637739110027.svg\" alt=\"\" width=\"339\" height=\"161\" \/><\/a><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]If we take the corresponding sides of the triangles and set up ratios, we would have:<br \/>\n<img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{10}{15}=\\frac{6}{9}=\\frac{8}{12}\" alt=\"\\fn_phv \\frac{10}{15}=\\frac{6}{9}=\\frac{8}{12}\" align=\"absmiddle\" \/><br \/>\nAll of the ratios reduce to a value of <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{2}{3}\" alt=\"\\fn_phv \\frac{2}{3}\" align=\"absmiddle\" \/>, thus giving us a scale factor of <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{2}{3}\" alt=\"\\fn_phv \\frac{2}{3}\" align=\"absmiddle\" \/>.<br \/>\nThe figures are therefore similar, and the similarity statement, placing corresponding angles in order, would be <span style=\"color: red;\"><strong>\u2206ABC ~ \u2206DEF<\/strong><\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Similarity Statement[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Which of the following is true when two figures are similar?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations\"><img loading=\"lazy\" class=\"alignnone wp-image-3647 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/11-25.png\" alt=\"Similarity Statement - Practice Problem 1\" width=\"288\" height=\"283\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Select the correct similarity statement for the figures below.<\/span><\/strong><br \/>\nIf figures are not similar, select the answer choice, “Not Similar”.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations\"><img loading=\"lazy\" class=\"alignnone wp-image-3649 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/12-17.png\" alt=\"Similarity Statement - Practice Problem 2\" width=\"299\" height=\"280\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">Select the correct similarity statement for the figures below.<\/span><\/strong><br \/>\nIf figures are not similar, select the answer choice, “Not Similar”.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations\"><img loading=\"lazy\" class=\"alignnone wp-image-3651 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13-16.png\" alt=\"Similarity Statement - Practice Problem 3\" width=\"298\" height=\"232\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 4<\/h5>\n<p><strong><span style=\"color: #16a085;\">Determine if the two figures are similar by using transformations.<\/span><\/strong><br \/>\nAre the figures similar?<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations\"><img loading=\"lazy\" class=\"alignnone wp-image-3654 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/14-10.png\" alt=\"Similarity Statement - Practice Problem 4\" width=\"295\" height=\"353\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/14-10.png 295w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/14-10-251x300.png 251w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similarity-and-transformations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]A <strong>similarity statement<\/strong> is a statement used in geometry to prove exactly why two shapes have the same shape and are in proportion.<\/p>\n<p><strong>Scale Factor<\/strong>: A scale factor is the ratio of the lengths of two corresponding sides of two similar polygons.<\/p>\n<p><strong>Similar<\/strong>: Figures that have the same shape, but not necessarily the same size.<\/p>\n<p><strong>Congruent<\/strong>: Figures that have the same shape and same size.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/congruence-and-transformations\"><span style=\"color: #ed5600;\">Congruence and Transformations <\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/congruence\"><span style=\"color: #ed5600;\">Congruence<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/dilation\"><span style=\"color: #ed5600;\">Dilation<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635249033104{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/properties-of-similar-polygons\"><span style=\"color: #333399;\">Properties of Similar Polygons<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/similar-triangles-and-indirect-measurement\"><span style=\"color: #333399;\">Similar Triangles and Indirect Measurement<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/slope-and-similar-triangles\"><span style=\"color: #333399;\">Slope and Similar Triangles<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/area-and-perimeter-of-similar-figures\"><span style=\"color: #333399;\">Area and Perimeter of Similar Figures<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Geometry and Spatial sense” color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fgeometry-and-spatial-sense|title:Geometry%20and%20Spatial%20sense||”][vc_btn title=”Graphs” color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fgraphs|title:Graphs||”][vc_btn title=”Trigonometry” color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Ftrigonometry|title:Trigonometry||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Similarity Statement [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Similarity is an important concept in geometry that helps prove some theorems and their corollaries. The statement of similarity is based on the fact that for two shapes to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Similarity Statement | Oryx Learning<\/title>\n<meta name=\"description\" content=\"Similarity is an important concept in geometry that helps prove some theorems and their corollaries....\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/similarity-statement\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Similarity Statement\" \/>\n<meta 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