Question

In triangles $ABC$ and $PQR$, $AB=AC$, $\angle C=\angle P$ and $\angle B=\angle Q$. Then the two triangles are :

• A. Isosceles but not congruent
• B. Isosceles and congruent
• C. Congruent but not isosceles
• D. Neither congruent nor isosceles

Answer 1

The correct option is A Isosceles but not congruent

In $△ABC$ and $△PQR$
$\angle C=\angle P$ (Given)
$\angle B=\angle Q$ (Given)
$\angle A=\angle R$ (Third angle of the triangle)
Thus, $△ABC\sim △PQR$
Also, given, $AB=AC$
Thus, $\angle B=\angle C$ (Isosceles triangle Property)
But, $\angle B=\angle Q$ and $\angle C=\angle P$
Hence, $\angle Q=\angle P$
or $PR=QR$
Thus, both the triangles are Isosceles but not congruent.