Question

Verify that QT is Parallel to RS using the triangle proportionality theorem.

Answer 1

The triangle proportionality theorem is

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

So to prove QT parallel to RS, we have to show

$\frac{PQ}{QR} = \frac{PT}{TS}$

Substituting the values, we will get

$\frac{18}{38} = \frac{36}{80} \\ 0.47368421=0.45$

Which are not equal, therefore the lines are not parallel .