Mathematics
In a triangle ABC, AB = AC. Show that the altitude AD is median also.
Triangles
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Answer
△ ABC is shown below:
In △ ABD and △ ACD,
⇒ AB = AC (Given)
⇒ ∠ADB = ∠ADC (Both equal to 90°)
⇒ AD = AD (Common side)
∴ ∆ ABD ≅ ∆ ACD (By R.H.S. axiom)
We know that,
Corresponding parts of congruent triangles are equal.
∴ BD = CD.
Hence, proved that altitude AD is median also.
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