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In Figure, PS is the bisector of ∠ QPR of ∆ PQR. Prove that QS/PQ = SR/PR Q.1

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How i solve the problem of class 10th of triangles chapter of exercise 6.6 of ncert of question no 1. How i solve this question because i don’t know how to solve it In Figure, PS is the bisector of ∠ QPR of ∆ PQR. Prove that QS/PQ = SR/PR

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  1. Let us draw a line segment RT parallel to SP which intersects extended line segment QP at point T.

    Given, PS is the angle bisector of ∠QPR. Therefore,

    ∠QPS = ∠SPR………………………………..(i)

    Ncert solutions class 10 chapter 6-64

    As per the constructed figure,

    ∠SPR=∠PRT(Since, PS||TR)……………(ii)

    ∠QPS = ∠QRT(Since, PS||TR) …………..(iii)

    From the above equations, we get,

    ∠PRT=∠QTR

    Therefore,

    PT=PR

    In △QTR, by basic proportionality theorem,

    QS/SR = QP/PT

    Since, PT=TR

    Therefore,

    QS/SR = PQ/PR

    Hence, proved.

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