Question

In the shown figure, PA perpendicular bisector AB and QB perpendicular AB. Further, AP = BQ. Prove that O is mid-point of Side AB and side PQ. ​

Answer 1

Answer:

In △OAP and △OBQ,

AP=BQ(given)

∠OAP=∠OBQ=90°

 ∠OAP=∠OBQ(vertically opposite angles)

∴△OAP is congruent to △OBQ by AAS axiom

∴OA=OB by C.P.C.T.

and OP=OQ by C.P.C.T

⇒O is the midpoint of line segments AB and PQ