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AnilSinghBora
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Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ΔPQR (see Fig 6.41). Show that ΔABC ~ ΔPQR. Q.12

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How i solve the problem of exercise 6.3 of class 10th math, of chapter Triangles, How i solve in easy way Please help me sir for solving this problem Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ΔPQR (see Fig 6.41). Show that ΔABC ~ ΔPQR.

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  1. Given, ΔABC and ΔPQR, AB, BC and median AD of ΔABC are proportional to sides PQ, QR and median PM of ΔPQR

    i.e. AB/PQ = BC/QR = AD/PM

    We have to prove: ΔABC ~ ΔPQR

    As we know here,

    AB/PQ = BC/QR = AD/PM

    Ncert solutions class 10 chapter 6-23

    ⇒AB/PQ = BC/QR = AD/PM (D is the midpoint of BC. M is the midpoint of QR)

    ⇒ ΔABD ~ ΔPQM [SSS similarity criterion]

    ∴ ∠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 equation (i) and (ii), we get,

    ΔABC ~ ΔPQR [SAS similarity criterion]

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