Question

Fig. 7.35
In Fig. 7.35, AP and BQ are perpendiculars to the line-segment AB and AP = BQ. Prove that O is
the midpoint of line-segment AB and PQ.​

Answer 1

Answer

In △APO and △BQO

AP=BQ [data]

∠POA=∠BOQ[V.O.A]

∠PAO=∠QBO=90⁰ [ AP & BQ are perpendiculars ]

∴△APO=△BQO [ AAS△ postulate ]

∴△AO=BO [ Corresponding sides ]

PO=OQ

∴O is the midpoint of AB and PQ