Question

Please Solve The Question!

Answer 1

ANSWER.

✦GIVEN

(1) AP=BQ=CR.

(2) angle PQR = 90°

✦PROVE.

(1)PB=QC

(2)QP=QR

(3)angle QPR=45°

✦PROOF .

PART ✍

(1). it is a square so all sides are equal

=>AB=CB. ( all side of square are equal)

=. AP+PB=BQ+QC

= BQ+PB=BQ+ QC ( given AP=BQ=CR)

= PB=QC.

PART 2 ✍

(2). In ∆PBQ and ∆RCQ

angle B= angle C. ( 90° Angles)

PB=QC. ( just prove)

BQ= CR. ( GIVEN)

=> ∆PBQ. congurant ∆RCQ

=> PB= RC=BQ=CQ=PQ=RQ

and all angle are equal

So. it mean RQ = PQ

=> angle RPQ= anglePQR (opposite angle
of equal side)

so
As. we know

☞SUM OF A ∆ IS EQUAL TO 180°

=> angle RPQ +angle QPR+angle PRQ=180°

let angle RPQ=x

=. x+anglePQR+x=180° ( angle RPQ=

anglePQR

= 2x+anglePQR=180°

=2x+90°=180°. ( angle PQR = 90°)

= 2x=90°

x=45°

=> angle QPR= 90°