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Question
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
Options
isosceles but not congruent
isosceles and congruent
congruent but not isosceles
neither congruent nor isosceles
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Solution
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.
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