In the given figure if AD ⊥ BC, prove that AB2 + CD2 = BD2 + AC2. – InterviewSolution

1.

In the given figure if AD ⊥ BC, prove that AB2 + CD2 = BD2 + AC2.

Answer»

Given: In △ABC, AD ⊥ BC.

R.T.P: AB² + CD² = BD² + AC²

Proof: △ABD is a right angled triangle

AB² – BD² = AD² ……. (1)

△ACD is a right angle triangle

AC² – CD² = AD^{2............ (2)}

From (1) and (2)

AB² – BD² = AC² – CD²

AB² + CD² = BD² + AC²

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