Question

State whether the following statement is true or false.

If a line segment $AB$ is bisected at point $P$ and through point $P$ another line segment $PQ$ which is perpendicular to $AB,$ is drawn then $QA=QB.$

• A. True
• B. False

Answer 1

The correct option is A True

Join QA and QB.

In $△PQA$ and $△PQB$,
$PQ=PQ$ (Common)
$\angle PQA=\angle PQB$ (Each ${90}^{\circ }$, PQ is perpendicular to AB)
$PA=PB$ (P bisects AB)

Thus, $△PAQ\cong △PBQ$
Hence, $QA=QB$ (By cpct)