Answer:
Line segment TU is parallel to line segment RS because 32/36 = 40/45
Step-by-step explanation:
In the figure attached, the problem is shown.
The side-splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally. In the context of this problem that means, if TU || RS then QT/TR = QU/US. The converse is if QT/TR = QU/US, then TU || RS.
From the picture:
QT = 32
TR = 36
QU = 40
US = 45
QT/TR = 32/36 = 8/9
QU/US = 40/45 = 8/9
then, the TU and RS are parallel
