Question

triangle p q r is an isosceles triangle in which pq equal to pr qp is produced to pt s qp equals to ps show that angle q r s equal to 90 degree ​

Answer 1

Step-by-step explanation:

Angle QPR=(180°-Angle SPR) (linear angles)

In triangle PQR,

Angle Q= Angle PRQ

A/Q

Angle Q+Angle PRQ+ Angle QPR=180°

or,Angle PRQ+ Angle PRQ+ (180°-Angle SPR)= 180°

or, 2×Angle PRQ+ 180°-Angle SPR= 180°

or, 2×Angle PRQ= 180°-180°+Angle SPR

or, 2×Angle PRQ= Angle SPR

hence, Angle PRQ=Angle SPR/2

In triangle SPR,

QP=PR=PS

So, Angle PSR=Angle PRS

A/Q,

Angle SPR+ Angle PSR+ Angle PRS= 180°

or, Angle SPR+ Angle PRS+ Angle PRS=180°

or, 2×Angle PRS=180°-Angle SPR

hence, Angle PRS=(180°-Angle SPR)/2

Now,

Angle QRS= Angle PRQ+ Angle PRS

= Angle SPR/2+ (180°-Angle SPR)/2

= (180°+ Angle SPR -Angle SPR)/2

=180°/2

=90°. Proved.

Answer 2

Answer:

u see in pic

Step-by-step explanation:

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