Question

In two triangles PQR and LMN, PQ = QR, $\angle$P = $\angle$M and QR = LN, then which of the following statements is CORRECT?

• A. Triangles are congruent only
• B. Triangles are isosceles only
• C. Triangles are both congruent and isosceles
• D. None of these

Answer 1

Answer: (D)

In $△PQR$ and $△LMN$

$\Rightarrow$ $PQ=QR$ and $QR=LN$

$\therefore$ $PQ=LN$

$\Rightarrow$ $\angle P=\angle M$

$\Rightarrow$ Here, only one side and one angle are equal, so these both triangle cannot be congruent.

$\Rightarrow$ Two angles in both triangles are also not equal so, triangles are not isosceles.

$\therefore$ Correct answer is option $D$.