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Question
Prove that the medians corresponding to equal sides of an isosceles triangle are equal.
Solution
In ΔABC,
AB = AC .......(Given)
∴ ∠C = ∠B ......(i) [angles opp. to equal sides are equal]
⇒ `1/2"AB" = 1/2"AC"`
⇒ BF = CE .........(ii)
In ΔBCE and ΔCBF,
∠C = ∠B .......[From (i)]
BF = CE .........[From (ii)]
BC = BC .......[Common]
∴ ΔBCE ≅ ΔCBF .......[SAS]
⇒ BE = CF .......[c.p.c.t.]
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