Question

In ΔABC and ΔPQR, ∠A = ∠P, ∠B = ∠Q and AB = 2 PQ, then the two triangles are ______.

Options

• congruent but not similar

• similar but not congruent

• neither congruent nor similar

• congruent and similar both

Answer 1

In ΔABC and ΔPQR, ∠A = ∠P, ∠B = ∠Q and AB = 2 PQ, then the two triangles are similar but not congruent.

Explanation:

Given ∠A = ∠P and ∠B = ∠Q, the two triangles are similar by AA (Angle–Angle) similarity.

Also, AB = 2 PQ, so corresponding sides are not equal (ratio is 2 : 1), hence triangles are not congruent.

Therefore, the triangles are similar but not congruent.