Question

In the given figure PB and PQ are equal perpendiculars on lines l and m, prove that:
∆APB ≅∆APQ

Answer 1

Given : PB and PQ are equal perpendiculars on lines l and m . A is intersection of line l & m

To Find :  prove that:  ∆APB ≅∆APQ

Solution:

comparing Δ APB  &  ΔAPQ

AP = AP   ( common )

PB = PQ   ( given )

∠ABP  = ∠ AQP  = 90°

=>  right angle triangle

Two right angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right angled triangle.

Hence

Δ APB  ≅ ΔAPQ

QED

Hence proved

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