Question

Use the converse of the side-splitter theorem to determine if . Which statement is true?

Line segment TU is parallel to line segment RS because .
Line segment TU is not parallel to line segment RS because .
Line segment TU is parallel to line segment RS because .
Line segment TU is not parallel to line segment RS because .

Answer 1

Line segment TU is parallel to line segment RS because 32/36 = 40/45

Answer 2

TU line segment is parallel to RS line segment because of 32/36 = 40/45.

The theorem related to side splitter interprets that if a line is parallel to a definite side of a triangle and happen to intersect the other two sides, then this line bisects those two sides in a definite proportion.

Each intersection,  to be equal, in that case, the lines becomes parallel.

The second is if the alternate internal angles, the angles that are located on opposite sides of the transversal and are located inside the parallel lines, are equal, then the lines become parallel.