Question

In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.

विकल्प

• isosceles but not congruent

• isosceles and congruent

• congruent but not isosceles

• neither congruent nor isosceles

Answer 1

In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are isosceles but not congruent.

Explanation:

In triangle ABC,

AB = AC   ...[Given]

∠C = ∠B   ...[Angle opposite to equal sides are equal]

So, in triangle ABC is an isosceles triangle.

∠B = ∠Q  ...[Given]

∠C = ∠P

∠P = ∠Q   ...[Since, ∠C = ∠B]

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

So, in triangle PQR is also an isosceles triangle.

Hence, both triangle are isosceles but not congruent.