Question

In $\Delta PQR$, PE is perpendicular bisector of $\angle QPR$, then :

• A. $QE=PE$
• B. $QP>QE$
• C. $PQ=PR$
• D. $PQ>PR$

Answer 1

The correct option is C $PQ=PR$

In $△PQE$ and $△PRE$

$PE=PE$ (common side)

$QE=RE$ (As $PE$ is perpendicular bisector)

$\angle PEQ=\angle PER$ (As $PE$ is the perpendicular bisector )

$\Rightarrow △PQE\cong PRE$ by $RHS$ criteria.

Corresponding parts of congruent triangles are equal

$\Rightarrow PQ=PR$