{"id":273,"date":"2022-04-13T10:32:01","date_gmt":"2022-04-13T10:32:01","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=273"},"modified":"2025-02-28T11:23:31","modified_gmt":"2025-02-28T11:23:31","slug":"n-6-transformations-that-carry-a-polygon-onto-itself","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/n-6-transformations-that-carry-a-polygon-onto-itself\/","title":{"rendered":"N.6 Transformations that carry a polygon onto itself"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Transformations that carry a polygon onto itself<\/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\">Reflecting&nbsp;a regular&nbsp;n-gon across a line of symmetry carries the&nbsp;n-gon onto&nbsp;itself.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">If&nbsp;n&nbsp;is odd, the lines of symmetry pass through a vertex and the midpoint of the opposite&nbsp;side.<\/li>\n\n\n\n<li class=\"has-large-font-size\">If&nbsp;n&nbsp;is even, the lines of symmetry either pass through two opposite vertices, or pass through the midpoints of two opposite&nbsp;sides.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">Rotating&nbsp;a regular&nbsp;n-gon by a multiple of&nbsp;360\u00b0\/n carries the&nbsp;n-gon onto&nbsp;itself.<\/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:#b8f8f8\"><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-61a787668a79c95ba7b4f89a90041cee\" style=\"color:#b00012\"><strong>Which&nbsp;of the following transformations carry this regular polygon onto&nbsp;itself?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-500px-4-2.png\" alt=\"\" class=\"wp-image-4669\" style=\"width:333px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-500px-4-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-500px-4-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-500px-4-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>a ) Rotation&nbsp;of&nbsp;90\u00b0&nbsp;clockwise<\/p>\n\n\n\n<p>b ) Reflection across \ud835\udcc1<\/p>\n\n\n\n<p>c ) Rotation&nbsp;of&nbsp;45\u00b0&nbsp;anticlockwise<\/p>\n\n\n\n<p>d ) Rotation&nbsp;of&nbsp;120\u00b0&nbsp;anticlockwise<\/p>\n<\/div><\/div>\n\n\n\n<p>This&nbsp;regular polygon has&nbsp;5&nbsp;sides, so it is a&nbsp;pentagon.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___4_-removebg-preview-4.png\" alt=\"\" class=\"wp-image-4671\" style=\"width:347px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___4_-removebg-preview-4.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___4_-removebg-preview-4-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___4_-removebg-preview-4-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>First,&nbsp;see if the reflection answer choice is correct. In other words, is&nbsp;\ud835\udcc1&nbsp;a line of&nbsp;symmetry? <\/p>\n\n\n\n<p>Since&nbsp;n=&nbsp;5&nbsp;is odd and&nbsp;\ud835\udcc1&nbsp;passes through a vertex and the midpoint of its opposite side,&nbsp;\ud835\udcc1&nbsp;is a line of symmetry. So, this answer choice is&nbsp;correct:<\/p>\n\n\n\n<p>reflection&nbsp;across&nbsp;\ud835\udcc1<\/p>\n\n\n\n<p>Second,&nbsp;see if any of the rotation answer choices are correct. Rotating a regular pentagon by a multiple of&nbsp;360\u00b0\/5=72\u00b0&nbsp;carries the pentagon onto itself. So, none of the rotation answer choices are&nbsp;correct.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#bcd2f8\"><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-61a787668a79c95ba7b4f89a90041cee\" style=\"color:#b00012\"><strong>Which&nbsp;of the following transformations carry this regular polygon onto&nbsp;itself?<\/strong><\/p>\n\n\n\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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-40.png\" alt=\"\" class=\"wp-image-11269\" style=\"width:386px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-40.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-40-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-40-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>a ) Rotation&nbsp;of&nbsp;90\u00b0&nbsp;clockwise<\/p>\n\n\n\n<p>b ) Rotation&nbsp;of&nbsp;120\u00b0&nbsp;anticlockwise<\/p>\n\n\n\n<p>c ) Rotation&nbsp;of&nbsp;90\u00b0&nbsp;anticlockwise<\/p>\n\n\n\n<p>d ) Reflection across \ud835\udcc1<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___7_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-4678\" style=\"width:372px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___7_-removebg-preview-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___7_-removebg-preview-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___7_-removebg-preview-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>First,&nbsp;see if the reflection answer choice is correct. In other words, is&nbsp;\ud835\udcc1&nbsp;a line of&nbsp;symmetry?<\/p>\n\n\n\n<p>Since&nbsp;n&nbsp;=&nbsp;3&nbsp;is odd and&nbsp;\ud835\udcc1&nbsp;passes through a vertex and the midpoint of its opposite side,&nbsp;\ud835\udcc1&nbsp;is a line of symmetry. So, this answer choice is&nbsp;correct:<\/p>\n\n\n\n<p>reflection&nbsp;across&nbsp;\ud835\udcc1<\/p>\n\n\n\n<p>Second,&nbsp;see if any of the rotation answer choices are correct. Rotating an equilateral triangle by a multiple of&nbsp;360\u00b0\/3=120\u00b0carries the equilateral triangle onto itself. So, this is the only correct rotation answer&nbsp;choice:<\/p>\n\n\n\n<p>rotation&nbsp;of&nbsp;120\u00b0&nbsp;anticlockwise<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f0acb7\"><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-61a787668a79c95ba7b4f89a90041cee\" style=\"color:#b00012\"><strong>Which&nbsp;of the following transformations carry this regular polygon onto&nbsp;itself?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-41.png\" alt=\"\" class=\"wp-image-11271\" style=\"width:249px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-41.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-41-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-41-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>a )  Reflection across \ud835\udcc1<\/p>\n\n\n\n<p>b ) Rotation&nbsp;of&nbsp;60\u00b0&nbsp;clockwise<\/p>\n\n\n\n<p>c ) Rotation&nbsp;of&nbsp;72\u00b0&nbsp;anticlockwise<\/p>\n\n\n\n<p>d ) Rotation&nbsp;of&nbsp;60\u00b0&nbsp;anticlockwise<\/p>\n<\/div><\/div>\n\n\n\n<p>This&nbsp;regular polygon has&nbsp;6&nbsp;sides, so it is a&nbsp;hexagon.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___9_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-4687\" style=\"width:389px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___9_-removebg-preview-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___9_-removebg-preview-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___500px___9_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>First,&nbsp;see if the reflection answer choice is correct. In other words, is&nbsp;\ud835\udcc1a line of&nbsp;symmetry?<\/p>\n\n\n\n<p>Since&nbsp;n=&nbsp;6&nbsp;is even and&nbsp;\ud835\udcc1&nbsp;passes through a vertex and a midpoint,&nbsp;\ud835\udcc1&nbsp;is not a line of symmetry. So, the reflection answer choice is not&nbsp;correct.<\/p>\n\n\n\n<p>Second,&nbsp;see if any of the rotation answer choices are correct. Rotating a regular hexagon by a multiple of&nbsp;360\u00b0\/6=60\u00b0&nbsp;carries the hexagon onto itself. So, these are the correct rotation answer&nbsp;choices:<\/p>\n\n\n\n<ul id=\"yui_3_18_1_1_1677491415827_906\" class=\"wp-block-list\">\n<li>rotation&nbsp;of&nbsp;60\u00b0&nbsp;clockwise<\/li>\n\n\n\n<li>rotation&nbsp;of&nbsp;60\u00b0&nbsp;anticlockwise<\/li>\n<\/ul>\n<\/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\/87639\/515\/766\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-87.png\" alt=\"\" class=\"wp-image-7109\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-87.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-87-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-87-150x150.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\/38046\/713\/752\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-105.png\" alt=\"\" class=\"wp-image-7110\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-105.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-105-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-105-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Transformations that carry a polygon onto itself Key Notes : Reflecting&nbsp;a regular&nbsp;n-gon across a line of symmetry carries the&nbsp;n-gon onto&nbsp;itself. Rotating&nbsp;a regular&nbsp;n-gon by a multiple of&nbsp;360\u00b0\/n carries the&nbsp;n-gon onto&nbsp;itself. Learn with an example Which&nbsp;of the following transformations carry this regular polygon onto&nbsp;itself? a ) Rotation&nbsp;of&nbsp;90\u00b0&nbsp;clockwise b ) Reflection across \ud835\udcc1 c ) Rotation&nbsp;of&nbsp;45\u00b0&nbsp;anticlockwise d )<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/n-6-transformations-that-carry-a-polygon-onto-itself\/\">Continue reading <span class=\"screen-reader-text\">&#8220;N.6 Transformations that carry a polygon onto itself&#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-273","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/273","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=273"}],"version-history":[{"count":15,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/273\/revisions"}],"predecessor-version":[{"id":17547,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/273\/revisions\/17547"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=273"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}