Maths-
General
Easy

Question

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

Hint:

Find the congruence rule used and then find the parallel sides.

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
    straight angle A O D equals straight angle B O C(vertically opposite angles)
    So by SAS congruence rule, we have
    ΔAOD ⩭ ΔBOC
    (ii) SinceΔAOD ⩭ ΔBOC, we have
    straight angle O A D equals straight angle O B C( Corresponding part of congruent triangles)
    But they form alternate interior angles and since they are equal,  AD || BC.

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