Question

Which of the following sides are equal if $\angle RPQ$ and $\angle RQP$ are similar?

• A. $RP=RQ$
• B. $RP=PQ$
• C. $RQ=PQ$
• D. None of these

Answer 1

Answer: (A)

The correct option is A $RP=RQ$
Here, since two angles of the triangle are equal, the $△RPQ$ is an isosceles triangle.

Then, from the converse of isosceles angle property,

sides opposite to equal angles of a triangle are equal.

Here, $RP$ is the side opposite to $\angle RQP$

and $RQ$ is the side opposite to $\angle RPQ$.

Thus, if $\angle RPQ=\angle RQP$, then $RP=RQ$ .

Therefore, option $A$ is correct.