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Side AB and BC and median …

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Side AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that ∆ABC ~ ∆ PQR

    • Posted by Ashish Kumar 5 years, 1 month ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Chandu G 5 years, 1 month ago

    AB/PQ = BC/QR = AD/PM To Prove: ΔABC ~ ΔPQR Proof: AB/PQ = BC/QR = AD/PM  AB/PQ = BC/QR = AD/PM (D is the mid-point of BC. M is the mid point of QR) ΔABD ~ ΔPQM [SSS similarity criterion] Therefore, ∠ABD = ∠PQM [Corresponding angles of two similar triangles are equal] ∠ABC = ∠PQR In ΔABC and ΔPQR AB/PQ = BC/QR ———(i) ∠ABC = ∠PQR ——-(ii) From above equation (i) and (ii), we get ΔABC ~ ΔPQR [By SAS similarity criterion] Hence Proved

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