Question

Prove that the medians corresponding to equal sides of an isosceles triangle are equal.

Answer 1

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.]