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06/06/2021 12:33 pm
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In Figure, PS is the bisector of ∠ QPR of ∆ PQR. Prove that QS/PQ = SR/PR
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06/06/2021 12:36 pm
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.
∠QPS = ∠SPR ………………..(i)
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
PT = PR
In △QTR, by basic proportionality theorem,
QS/SR = QP/PT
Since, PT = TR
QS/SR = PQ/PR
Hence, proved.
This post was modified 4 years ago by Raavi Tiwari