Question

ΔABC is isosceles in which AB = AC. Seg BD and seg CE are medians. Show that BD = CE.

Answer 1

We have,

AB=AC & AD = AE (Isoceles Triangle)

ANGLE A = ANGLE A ( common angle)

Now, 

AB=AC
1/2 (AB) = 1/2 (AC)
As, D is the mid-point of AC and E is the mid-point of AB.
ΔABDis congruent to ΔACE by SAS congruence rule.

So, BD = CE (Corresponding parts of congruent triangles are congruent)