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Question

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.

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