Question

In ∆ABC and ∆PQR, if AB = AC, ∠C = ∠P and ∠B = ∠Q, then the two triangles are:

• A. Isosceles but not congruent
• B. Isosceles and congruent
• C. Congruent but not isosceles
• D. Neither congruent not isosceles

Answer 1

The correct option is A

Isosceles but not congruent

In ∆ABC,

AB = AC (given)

⇒ ∠C = ∠B [angles opposite to equal sides are equal]

So, ∆ABC is an isosceles triangle.

But it is given that ∠B = ∠Q

∠C = ∠P

∠P = ∠Q

QR = PR [Sides opposite to equal angles are equal]

So, ∆PQR is also an isosceles triangle.

Therefore, both triangles are isosceles but not congruent. As, we know that AAA is not a criterion for congruence of triangles.