Question

in the figure given below, PQ and RS are perpendicular to QS, QA =BS and PB =AR. prove that angle QPB =angleSRA

Answer 1

here is your solution

Answer 2

∠QPB = ∠SRA

GIVEN

PQ⏊ QS

RS⏊ QS

QA = BS

PB= AR

TO PROVE

∠QPB = ∠SRA

SOLUTION

We can simply solve the above problem as follows;

In ΔPQB and ΔSRA

∠PQB = ∠RSA = 90°

QA = SB (Given)

QA + AB = SB + AB (Euclid's axiom)

So,

QB = SA

PB = AR (Given)

According to Right angle - Hypotenuse- side Congruence rule;

ΔPQB ≈ ΔSRA

Therefore,

∠QPB = ∠SRA (Corresponding angle of congruent triangles are equal)

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