Question

In figure,angleQPS=angleRPT And anglePST=anglePQR And hence find the ratio ST : PT,if PR : QR=4:5

Answer 1

Answer:

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.

Answer 2

Solution:-

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.