Question 10
In ΔABC and ΔPQR, if AB=AC,∠C=∠P and ∠B=∠Q. The two triangles are
(A) isosceles but not congruent
(B) isosceles and congruent
(C) congruent but not isosceles
(D) neither congruent nor isosceles
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Solution
In ΔABC AB =AC [given] ⇒∠C=∠B [angles opposite to equal sides are equal]
so ΔABC is an isosceles triangle
But it is given that ∠B=∠Q ∠C=∠P ∴∠P=∠Q[∵∠C=∠B] ⇒QR=PR [sides opposite to equal angles are equal]
So, ΔPQR is also an isosceles traingle
Therefore, both triangles are isosceles but not congruent. As, we know that AAA is not a criterion for congruence of triangles.