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Question

ΔABC is an isosceles triangle such that AB=AC, prove that the altitude AO from A on BC bisects BC.

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Solution

In the right triangles AOB and AOC,
AOB=AOC = 90 degree
AB=AC (Since ΔABC is an isosceles)
AO=OA
Therefore, ΔAOBΔAOC by RHS congruence condition.
So, BO and CO are corresponding parts of congruence triangles.
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