Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:
(i) AOD ⩭ BOC
(ii)  AD || BC

The correct answer is: AD || BC.

(i) In ΔAOD and ΔBOC, we have
AO = OB (given)
OD = OC (given)
Since CD and AB intersects, we have
(vertically opposite angles)
So by SAS congruence rule, we have
ΔAOD ⩭ ΔBOC
(ii) SinceΔAOD ⩭ ΔBOC, we have
( Corresponding part of congruent triangles)
But they form alternate interior angles and since they are equal,  AD || BC.