Question

△ABC and △PQR are congruent to each other.

Assertion (A): Triangles ABC and PQR are similar to each other.

Reason (R): Two similar triangles are congruent 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

A is true, R is false.

Explanation:

Given, Δ ABC and Δ PQR are two congruent triangles.

Corresponding angles and sides are equal.

⇒ ∠A = ∠P, ∠B = ∠Q and ∠C = ∠R

∴ Δ ABC ∼ Δ PQR (By AAA postulate)

So, assertion (A) is true.

Similar triangles have the same shape but not necessarily the same size.

Congruent triangles have the same shape and size.

Size can be different in similar triangles but it has to be same in congruent triangles.

So, reason (R) is false.