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
[tex]\frac{PQ}{QR} = \frac{PT}{TS}[/tex]
Substituting the values, we will get
[tex]\frac{18}{38} = \frac{36}{80}
\\
0.47368421=0.45[/tex]
Which are not equal, therefore the lines are not parallel .
