SideAB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ?PQR (check image). Show that ΔABC ~ ΔPQR




  • August 17, 2020

    Given two triangles, ΔABC and ΔPQR in which AB, BC and median AD of ΔABC are proportional to sides PQ, QR and median PM of ΔPQR

    AB/PQ = BC/QR = AD/PM

    To Prove: ΔABC ~ ΔPQR

    We have? AB/PQ = BC/QR = AD/PM (D is the mid-point of BC. M is the midpoint 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 the above equation (i) and (ii), we get

    ΔABC ~ ΔPQR [By SAS similarity criterion]


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