Question

In triangle ABC, ∠BAC = 90° and AD is perpendicular to side BC. Triangle ABD is similar to triangle CBA by ______.

Options

• SAS

• ASA

• AAA

• RHS

Answer 1

In triangle ABC, ∠BAC = 90° and AD is perpendicular to side BC. Triangle ABD is similar to triangle CBA by AAA.

Explanation:

In △ CBA and △ ABD,

⇒ ∠CAB = ∠ADB (Both equal to 90°)

⇒ ∠CBA = ∠DBA (Common angles)

Since, two angles of two triangles are equal so third angle of both the triangle will also be equal.

⇒ ∠ACB = ∠DAB.

∴ △ CBA ~ △ ABD (By A.A.A. postulate)