Question

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.

If the above statement is true then mention answer as 1, else mention 0 if false

Answer 1

Given: PQ bisects AB and $PQ\perp AB$
Construction: Join QA and QB
To prove: $QA=QB$
In $△QAP$ and $△QBP$
$\angle QPA=\angle QPB$ (Each ${90}^{\circ }$)
$PA=PB$ (PQ bisects AB)
$PQ=PQ$ (Common)
thus, $△QAP\cong △QBP$ (SAS rule)
Thus, $QA=QB$ (By cpct)