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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. Show that : QA =QB. 


Solution

According to given information , we get our figure , As :


Now

In Δ APQ  and ∆ BPQ 

AP  =   BP                            ( As given AB is bisect at point P )

∠APQ    =  ∠ BPQ             ( As given PQ is perpendicular to AB )

And

PQ   = PQ                            ( Common side )

SO,

ΔAPQ ≅∆ BPQ               (  By  SAS  rule )

Hence

AQ    =   BQ                        (  by  CPCT )                              ( Hence proved )

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