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

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1.

In AD⊥BC, prove that AB2 + CD2 = BD2 + AC2.

Answer»

From ΔADC, we have

AC² = AD² + CD² … (1)

(Pythagoras theorem)

From ΔADB, we have

AB² = AD² + BD² … (2)

(Pythagoras theorem)

Subtracting (1) from (2) we have,

AB² – AC² = BD² – CD²

AB² + CD² = BD² + AC²

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