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Question:
Prove that median and altitude being equal in congruent triangles.
Answer:

We have to prove that altitude and median overlap (equal).
Then, we have to prove that angle ADC = ADB =90 degree. 
So, the triangle ADC is congruent to triangle ADB. 
Therefore by CPCT,
angle ADC = angle ADB =90 degree. 
We can also use SAS because angles opposite to equal sides are equal.

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