Question

In figure, PS/SQ = PT/TR and ∠PST = ∠PRQ.
Prove that ΔPQR is isosceles triangle.


Solve with complete steps and reasoning.

Answer 1

Hi ,

It is given that ,

PS / SQ = PT /TR a and

<PST = <PRQ

RTP : ∆PQR is isoseceles.

Proof :

In ∆PQR

PS/SQ = PT/TR

Therefore ,

ST // QR [ By converse of Thales Theorem ]

Now ,

ST // QR , PQ is the transversal ,

<PST = <PQR ---( 1 )

[ corresponding angles ]

<PST = <PRQ ( given ) ----( 2 )

from ( 1 ) and ( 2 ) ,

<PQR = <PRQ ---( 3 )

In triangle PQR ,

<PQR = <PRQ

Therefore ,

PR = PQ

[ sides opposite to equal angles are equal ]

∆ PQR is isoseceles.

Hence proved.

I hope this helps you.

: )

Answer 2

Refer the attachment.