Question

LE PETIT

55:48

Use the converse of the side-splitter theorem to determine if

TU || RS. Which statement is true?

Line segment TU is parallel to line segment RS because

Q

«

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

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Answer 1

Explanation:

T=s32.56

Answer 2

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

Explanation:

In the figure attached, the problem is shown.

The side-splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally. In the context of this problem that means, if TU || RS then QT/TR = QU/US. The converse is if QT/TR = QU/US, then TU || RS.

From the picture:

QT = 32

TR = 36

QU = 40

US = 45

QT/TR = 32/36 = 8/9

QU/US = 40/45 = 8/9

then, the TU and RS are parallel