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
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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