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?
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.

Answer 1

The statement  that is true is option A that  is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

What is the line segment about?

The law of the side- splitter connote that when f the line is parallel to a side of the triangle and if that said line do intersects the other 2 sides, tt is said to divides those  given sides proportionally.

So the converse means that when the sides are proportional so therefore, the side TU is said to be parallel to the side RS.

Thus;

$\frac{QT}{TR}$ = $\frac{32}{36} = \frac{8}{9}$

$\\\frac{QU}{US} =\frac{40}{45} = \frac{8}{9}$

Therefore,  the ratios are equal and as such TU is parallel to RS

Hence, The statement  that is true is option A that  is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

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