Intercept Theorem

Q.

$\frac{PS}{SQ}$ = $\frac{PT}{TR}$ and $\angle$PST = $\angle$PRQ. Prove that $\Delta$ PQR is an isosceles triangle.

Q.

In the follow diagram, lines l, m and n are parallel to each other. Two transversals p and q intersect the parallel lines l, m and n at points A, B, C and P, Q, R respectively as shown below.
Which of the following is correct?

1. $\frac{CB}{BA}=\frac{PQ}{QR}$

2. $\frac{AB}{BC}=\frac{PQ}{QR}$

3. $\frac{AB}{QR}=\frac{PQ}{BC}$

4. $\frac{AB}{PQ}=\frac{PQ}{BC}$

Q.

In figure shown below, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ. Then $\Delta$PQR is a/an __ triangle.

Q.

In below shown figure, $\frac{PS}{SQ}=\frac{PT}{TR}$ and$\angle PST=\angle PRQ$. Then $\Delta$PQR is an __ triangle.

Q. In the figure shown below , if $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ, then $\Delta$PQR is a/an triangle.

1. isosceles
2. equilateral
3. right angled
4. scalene

Q.

In below shown figure, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ. Then $\Delta$PQR is __ Triangle.

Q.

In the figure shown below, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ. Then $\Delta$PQR is an__ triangle.