Question

AP and BQ are perpendicular to AB. It is also given that AP = BQ. Prove that , O is the mind - point of the line segment AB = 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

Answer 2

Answer:

Step-by-step explanation:

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.

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