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