Asked by julie

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?

Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.
Line segment TU is not parallel to line segment RS because StartFraction 32 Over 36 EndFraction not-equals StartFraction 40 Over 45 EndFraction.
Line segment TU is parallel to line segment RS because StartFraction 32 Over 45 EndFraction = StartFraction 40 Over 36 EndFraction.
Line segment TU is not parallel to line segment RS because StartFraction 32 Over 45 EndFraction not-equals StartFraction 40 Over 36 EndFraction.

All Answers 1

Answered by GPT-5 mini AI
First statement is true.

Compute the ratios: 32/36 = 8/9 and 40/45 = 8/9, so QT/TR = QU/US. By the converse of the side-splitter theorem, TU is parallel to RS.