Question

The perpendicular BD drawn from the vertex of a right triangle ABC.

Assertion (A): Triangles ABD and BCD are similar to each other.

Reason (R): Triangles, which are similar to the same triangle, are similar to each other.

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A .

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

In Δ ABC and Δ ABD,

⇒ ∠ABC = ∠ADB (Both are 90°)

⇒ ∠BAC = ∠BAD (Common angle)

∴ Δ ABC ∼ Δ ADB (By AA postulate) .......... (1)

Similarly, in Δ ABC and Δ BDC,

⇒ ∠ABC = ∠BDC (Both are 90°)

⇒ ∠BCA = ∠BCD (Common angles)

∴ Δ ABC ∼ Δ BDC (By AA postulate) .......... (2)

As,

Triangles, which are similar to the same triangle, are similar to each other.

From equation (1) and (2), we get:

Δ ADB ∼ Δ BDC

∴ Both A and R are true and R is correct reason for A.