{"id":11274,"date":"2022-07-01T00:46:51","date_gmt":"2022-06-30T19:16:51","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11274"},"modified":"2022-07-01T00:46:52","modified_gmt":"2022-06-30T19:16:52","slug":"e-and-f-are-points-on-the-side-pq-and-pr-respectively-of-a-triangle-pqr-for-each-of-the-following-cases-state-whether-ef-qr","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/e-and-f-are-points-on-the-side-pq-and-pr-respectively-of-a-triangle-pqr-for-each-of-the-following-cases-state-whether-ef-qr\/","title":{"rendered":"E and F are points on the side PQ and PR respectively of a triangle PQR. For each of the following cases state whether EF || QR"},"content":{"rendered":"
E and F are points on the side PQ and PR respectively of a triangle PQR. For each of the following cases state whether EF || QR :<\/p>\n
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(i)<\/strong>\u00a0 PE = 3.9 cm,\u00a0 EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm<\/p>\n (ii)<\/strong>\u00a0 PE = 4cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm<\/p>\n (iii)<\/strong>\u00a0 PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm<\/p>\n By converse of basic\u00a0 proportionality theorem or Thales theorem <\/strong>that \u00a0if a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.<\/p>\n (i)<\/strong>\u00a0 Here, \\(PE\\over EQ\\) = \\(3.9\\over 3\\) = \\(1.3\\over 1\\)<\/p>\n \\(PF\\over FR\\) = \\(3.6\\over 2.4\\) = \\(3\\over 2\\) = 1.5<\/p>\n Thus, \\(PE\\over EQ\\) \\(\\ne\\) \\(PF\\over FR\\)<\/p>\n No, EF is not parallel to QR.<\/strong><\/p>\n (ii)<\/strong>\u00a0 Here, \\(PE\\over EQ\\) = \\(4\\over 4.5\\)<\/p>\n \\(PF\\over FR\\) = \\(8\\over 9\\) = \\(4\\over 4.5\\)<\/p>\n Thus, \\(PE\\over EQ\\) = \\(PF\\over FR\\)<\/p>\n Yes, EF is parallel to QR.<\/strong><\/p>\n (iii)<\/strong>\u00a0 Here, \\(PQ\\over PE\\) = \\(1.28\\over 0.18\\)<\/p>\n \\(PR\\over PF\\) = \\(2.56\\over 0.36\\) = \\(1.28\\over 0.18\\)<\/p>\n Thus, \\(PQ\\over PE\\) \\(\\ne\\) \\(PR\\over PF\\)<\/p>\n Yes, EF is parallel to QR.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" Question : E and F are points on the side PQ and PR respectively of a triangle PQR. For each of the following cases state whether EF || QR : (i)\u00a0 PE = 3.9 cm,\u00a0 EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm (ii)\u00a0 PE = 4cm, QE = 4.5 …<\/p>\nSolution :<\/h2>\n