Question

Triangle R Q S is cut by line segment T U. Line segment T U goes from side Q R to side Q S. The length of Q T is 32, the length of T R is 36, the length of Q U is 40, and the length of U S is 45.

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

Answer 1

A

Explanation:

Answer 2

the first statement is true

Explanation:

The side- splitter states that if the line is parallel to a side of the triangle and it intersects the other 2 sides, it divides those sides proportionally.

Thus the converse is that if the sides are proportional then the side TU is parallel to the side RS

Calculating the ratios

`(QT)/(TR)` =
`(32)/(36)` =
`(8)/(9)`

`(QU)/(US)` =
`(40)/(45)` =
`(8)/(9)`

Since the ratios are equal then TU is parallel to RS