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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 .

Use the converse of the side-splitter theorem to determine if . Which statement is-example-1

2 Answers

6 votes

Answer:

The answer to this question is the first option:

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

User Teagan
by
8.7k points
6 votes

Answer:

The correct option is 1.

Explanation:

From the given figure it is clear that QT=32, TR=36, QU=40 and US=45.

The converse of side splitter theorem states that if a line divides two sides proportionally, then that line is parallel to the third side.

The ratio in which TU divides the two sides is


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


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


(QT)/(TR)=(QU)/(US)=(8)/(9)

It means the line TU divides two sides proportionally.

Using converse of side splitter theorem, Line segment TU is parallel to line segment RS because


(32)/(36)=(40)/(45)

Therefore the correct option is 1.

User Ahmed HENTETI
by
7.8k points
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