In triangles ABC and PQR, 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
[A]
Solution. We know that, angles opposite to equal sides are equal
AB = AC
B = C
We also know that, sides opposite to equal angles are also equal
Here,Q =P
PR = QR
Hence, two sides of both the triangles are respectively equal.
So ABC and PQR are isosceles triangle.
But may or may not be congruent.
Because sides of ABC may not be equal to side of PQR.
Hence option (A) is correct.