{"id":11321,"date":"2022-07-07T18:29:10","date_gmt":"2022-07-07T12:59:10","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11321"},"modified":"2022-07-07T18:29:14","modified_gmt":"2022-07-07T12:59:14","slug":"state-which-pairs-of-triangle-in-the-figure-are-similar-write-the-similarity-criterion-used-by-you-for-answering-the-question-and-also-write-the-pairs-of-similar-triangles-in-the-symbolic-form","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/state-which-pairs-of-triangle-in-the-figure-are-similar-write-the-similarity-criterion-used-by-you-for-answering-the-question-and-also-write-the-pairs-of-similar-triangles-in-the-symbolic-form\/","title":{"rendered":"State which pairs of triangle in the figure, are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :"},"content":{"rendered":"
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(i)<\/strong>\u00a0 In triangles ABC and PQR, we observe that<\/p>\n \\(\\angle\\) A = \\(\\angle\\) B = 60,<\/p>\n \\(\\angle\\) P = \\(\\angle\\) Q = 80<\/p>\n and \\(\\angle\\) C = \\(\\angle\\) R = 40<\/p>\n \\(\\therefore\\)\u00a0 By AAA criterion of similarity, \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR<\/strong><\/p>\n (ii)<\/strong>\u00a0 In triangles ABC and PQR, we observe that<\/p>\n \\(AB\\over QR\\) = \\(BC\\over RP\\) = \\(CA\\over PQ\\) = \\(1\\over 2\\)<\/p>\n \\(\\therefore\\)\u00a0 By SSS criterion of similarity, \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR<\/strong><\/p>\n (iii)<\/strong>\u00a0 In triangles LMP and DEF, we observe that the ratio of the sides of these triangles are not equal.<\/p>\n So, the two triangles are not similar.<\/strong><\/p>\n (iv)<\/strong>\u00a0 In triangles MNL and QPR, we observe that \\(\\angle\\) M = \\(\\angle\\) Q = 70<\/p>\n But, \\(MN\\over PQ\\) \\(\\ne\\) \\(ML\\over PR\\)<\/p>\n So, these\u00a0two triangles are not similar<\/strong>\u00a0as they do not satisfy the SAS criterion for similarity.<\/p>\n (v)<\/strong>\u00a0 In triangles ABC and FDE, we observe that \\(\\angle\\) A = \\(\\angle\\) F = 80<\/p>\n But, \\(AB\\over DE\\) \\(\\ne\\) \\(AC\\over DF\\)<\/p>\n So, these two triangles are not similar<\/strong> as they do not satisfy the SAS criterion for similarity.<\/p>\n (vi)<\/strong>\u00a0 In triangles DEF and PQR, we observe that<\/p>\n \\(\\angle\\) D = \\(\\angle\\) P = 70,<\/p>\n \\(\\angle\\) E = \\(\\angle\\) Q = 80<\/p>\n \\(\\therefore\\)\u00a0 By AAA criterion of similarity, \\(\\triangle\\) DEF ~ \\(\\triangle\\) PQR<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" Solution : (i)\u00a0 In triangles ABC and PQR, we observe that \\(\\angle\\) A = \\(\\angle\\) B = 60, \\(\\angle\\) P = \\(\\angle\\) Q = 80 and \\(\\angle\\) C = \\(\\angle\\) R = 40 \\(\\therefore\\)\u00a0 By AAA criterion of similarity, \\(\\triangle\\) ABC ~ \\(\\triangle\\) PQR (ii)\u00a0 In triangles ABC and PQR, we observe that \\(AB\\over QR\\) …<\/p>\n