Question

In triangle ABC, ∠B = 90° and in triangle ADE, ∠D = 90°.

Statement (1): \[\frac{AB}{AD} = \frac{AC}{AE}\]

Statement (2): Triangles AED and ACB are similar.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

In Δ ADE and Δ ABC,

⇒ ∠DAE = ∠BAC (Common angle)

⇒ ∠ADE = ∠ABC (Both are 90°)

∴ Δ ADE ∼ Δ ABC (By AA postulate)

We know that,

Corresponding sides of similar triangles are proportional.

⇒ `(AD)/(AB) = (AE)/(AC)`

⇒ `(AB)/(AD) = (AD)/(AE)`

So, both the statements are true.