In Fig. 6.50, if AD⟂BC, prove that AB2 + CD2 = BD2 + AC2. – InterviewSolution

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1.

In Fig. 6.50, if AD⟂BC, prove that AB2 + CD2 = BD2 + AC2.

Answer»

From ΔADC, we have

AC² = AD² + CD² (Pythagoras Theorem) .... (1)

From ΔADB, we have

AB² = AD² + BD² (Pythagoras Theorem) ......(2)

Subtracting (1) from (2), we have

AB² – AC² = BD²– CD²

or, AB² + CD²= BD² + AC²

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