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  • In triangles ABC and PQR, AB = AC, \angleC = \angleP and \angleB =\angleQ. The two triangles are (A) isosceles but not congruent (B) isosceles and congruent (C) congruent but not isosceles (D) neither congruent nor isosceles

In triangles ABC and PQR, AB = AC, \angleC = \angleP and \angleB =\angleQ. The two triangles are

(A) isosceles but not congruent

(B) isosceles and congruent

(C) congruent but not isosceles

(D) neither congruent nor isosceles

Answers (1)

[A]

Solution.         We know that, angles opposite to equal sides are equal

\because AB = AC

\Rightarrow \angleB = \angleC

We also know that, sides opposite to equal angles are also equal

Here,\angleQ =\angleP

\Rightarrow PR = QR

Hence, two sides of both the triangles are respectively equal.

So \triangleABC and \trianglePQR are isosceles triangle.

But may or may not be congruent.

Because sides of \triangleABC may not be equal to side of \trianglePQR.

Hence option (A) is correct.

Posted by

infoexpert24

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