PS is the bisector of angle QPR of triangle QPR.Prove that QS / SR=PQ / PR

Asked by Mdivya | 12th Mar, 2009, 11:04: AM

Expert Answer:

Construction: From R, draw a line parallel to PS which meets QP produced ar T.

Now PS || TR and PR is transversal.

Hence, angle SPR =  angle PRT (alternate interior angles)

PS || TR and PT is transversal.

Hence, angle QPS = angle QTR (corresponding angles)

But, angle QPS = angle SPR (PS bisects angle QPR)

So, angle PRT = angle QTR

So triangle PTR is isosceles triangle

So. PT = PR

Now, in triangle QTR

SP || RTHence, by Basic proportionality theorem,

QS / SR = QP / PT

Hence, QS / SR = QP / PR  Hence, pvd

Answered by  | 12th Mar, 2009, 12:57: PM

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