Question

60. In A ABC, PQIBC and AD is the median, prove that PE = EQ.
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Answer 1

Given : ΔABC, PQIBC and AD is the median  

To Find : prove that PE = EQ.

Solution:

Compare ΔAPQ  & ΔABC

∠A = ∠A  ( common)

∠P = ∠B  ( Corresponding angle )

∠Q = ∠C ( Corresponding angle )

=> ΔAPQ ≈ ΔABC

AP/AB = PQ/BC   = AQ/AC

Similarly

ΔAPE  & ΔABD

=> AP/AB = PE/BD   = AE/AD

Similarly

ΔAQE  & ΔACD

=> AQ/AC = EQ/CD   = AE/AD

PE/BD   = AE/AD

EQ/CD   = AE/AD

=> PE/BD   =  EQ/CD

BD = CD  as AD is the median

=> PE = EQ

QED

Hence proved

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