Question

In the given figure, in ΔABC, BD and CE are perpendiculars to AC and AB respectively. Prove that: AE × BD = AD × CE.

Answer 1

Given that: In ΔABC, BD and CE are perpendicular to AC and AB respectively.

To Prove: AE × BD = AD × CE

Proof: In ΔADB and ΔAEC

∠A =∠A     ...[Common]

∠ADB = ∠AEC    ...[Each 90°]

⇒ ΔADB ∼ ΔAEC

When two triangles are similar, then their corresponding sides are proportional.

So, `(BD)/(CE) = (AD)/(AE)`

Hence, BD × AE = AD × CE