{"id":5855,"date":"2013-05-07T05:32:31","date_gmt":"2013-05-07T05:32:31","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=5855"},"modified":"2014-12-02T08:27:02","modified_gmt":"2014-12-02T08:27:02","slug":"congruent-figures","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/05\/07\/congruent-figures\/","title":{"rendered":"Congruent Figures"},"content":{"rendered":"

Overview:\u00a0 What Are Congruent Figures?<\/strong>
\nGeometric figures are congruent if they have exactly the same size and shape.\u00a0 This means that their sides are all the same size and their angles are all the same measurements.\u00a0 They differ from similar figures, in that similar figures have angles with the same measurement,\u00a0 but the measurement of side segments are\u00a0 in the same ratio.<\/p>\n

Transforming Similar Figures into Congruent Figures<\/strong>
\nSimilar figures can be transformed into congruent figures by making the smaller figure the same size as the larger figure or the larger figure the same size as the smaller figure.\u00a0 For example, suppose in the similar triangles \u2206ABC and \u2206DEF, the corresponding angles are all equal and the corresponding sides for \u2206DEF measure 4, 5, and 6.\u00a0 The corresponding sides for \u2206ABC are 8, 10, 12.\u00a0 To make the two triangles congruent, multiply the measurement of each side of \u2206DEF by 2, so that the new measurement of \u2206D’E’F’ is now 8, 10, 12 and the triangles are congruent.<\/p>\n

Special Properties of Triangles<\/strong>
\nWhen two triangles are congruent, there are six congruent relationships:\u00a0 three equal sides and three equal angles.\u00a0 However, triangles already have some special properties that make it possible to simplify those relationships, so that one does not have to look at all six relationships.\u00a0 The angles of all triangles in normal space add up to 1800<\/sup>, so that if one has two measurements of angles in a triangle, the third can be deduced by subtracting the other two from 180.\u00a0 The length of sides also have special relationships with the size of angles in normal space.<\/p>\n

Congruence Properties<\/strong>
\nThere are three properties of congruent triangles that one can use to determine if triangles are congruent, known as\u00a0 Side-Angle-Side (SAS),\u00a0 Side-Side-Side (SSS), and Angle-Side-Angle (ASA). In Side-Angle-Side, if two sides and the angle between them are congruent in both triangles, then the angles are congruent.\u00a0 In Side-Side-Side, if all three sides of one triangle are the same length as all three sides of another triangle, then the triangles are congruent.\u00a0\u00a0\u00a0 \u00a0In Angle-Side-Angle, if two angles of both triangles, as well as the common side between the angles they both share, are congruent , then the triangles are congruent.<\/p>\n

Example of Congruence in Action<\/strong>
\nhttps:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/2012\/10\/congruent.jpg<\/a><\/p>\n

For example, in the above figure, triangles \u2206PQR and \u2206LMN are congruent.\u00a0 According to Side-Angle-Side, this means that the segments PQ and QR are equal to LM and MN and angles Q and M are equal, as well as the segments QR and RP to MN and NL and angles R and N are equal.\u00a0 In addition RP and PQ are equal to LN and LM and angles P and L are equal.\u00a0 According to Side-Side-Side, PQ, QR, and RP are equal to LM, MN, and NL.\u00a0 According to Angle-Side-Angle, angles R and P and segment RP are equal to angles N and L and segment NL, angles P and Q and segment PQ are equal to angles L and M and segment LM, and angles Q and R and segment QR are equal to angles M and N and segment MN.<\/p>\n

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Overview:\u00a0 What Are Congruent Figures? Geometric figures are congruent if they have exactly the same size and shape.\u00a0 This means that their sides are all the same size and their angles are all the same measurements.\u00a0 They differ from similar figures, in that similar figures have angles with the same measurement,\u00a0 but the measurement of […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10],"tags":[145,376,411,412,1586,1720],"class_list":["post-5855","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-asa","tag-congruent-triangles","tag-corresponding-angles","tag-corresponding-sides","tag-sas","tag-sss"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5855","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=5855"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5855\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5855"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}