Question

Given that ps/sq=pt/tr and angle pst= angle prq. prove that pqr is an isosceles triangle.

Answer 1

Hey,

It is given that PS/SQ = PT/TR
So, ST II QR (According to B.P.T)
Therefore, ∠ PST = ∠ PQR (Corresponding angles)
Also it is given that ∠ PST  = ∠ PRQ
So, ∠ PRQ = ∠ PQR
Therefore, PQ = PR ( sides opposite the equal angles)
So, Δ PQR is an isosceles triangle. 
Hence proved.

HOPE IT HELPS YOU:-))

Answer 2

Step-by-step explanation:

Given:

• In ∆PQR , PS/SQ = PT/TR and
• ∠PST is equal to ∠PRQ

To Prove:

• PQR is an isosceles triangle.

Proof: In ∆PQR , since PS/SQ = PT/TR therefore by Basic Proportionality Theorem or Thales' Theorem line ST will be parallel to QR

➯ ST || QR ( By BPT)

Now, If ST || QR therefore,

• ∠PQR = ∠PST ( Corresponding angles )............1

also,

• ∠PST = ∠PRQ ( given )..........2

So, From equation (1) and (2) we got

➨ ∠PQR = ∠PRQ

As we know that " Sides opposite to equal angles are also equal to each other "

Hence, PQ = PR

$\large\boxed{\texttt{Proved}}$