Using Triangle Similarity Theorems — Quiz

Question 67 • CMS 2026-2027 Foundations of Math 3 INITIAL CREDIT

Use the converse of the side-splitter theorem to determine if mathrm cap t cap u is parallel to mathrm cap r cap s Which statement is true?

Answer

Line segment TU is not parallel to line segment RS because 32 over 45 is not equal to 40 over 36 .

Line segment TU is parallel to line segment RS because 32 over 45 is equal to 40 over 36 .

Line segment TU is parallel to line segment RS because 32 over 36 is equal to 40 over 45 .

Line segment TU is not parallel to line segment RS because 32 over 36 is not equal to 40 over 45 .

Explanation

By the converse of the side-splitter theorem, the line segments are parallel when they divide the two sides proportionally. Here, 32/36 = 8/9 and 40/45 = 8/9, so the ratios are equal. Therefore, TU is parallel to RS, as stated in choice B.

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