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.

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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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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.

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 )