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When a transversal cuts two lines, several conditions can determine if the lines are parallel.

Which of the following statements is false?

A. When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.

B. When a transversal cuts two lines, such that pairs of alternate interior angles are equal, then the lines have to be parallel.

C. When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, then the lines have to be parallel.

D. When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are complementary, then the lines have to be parallel.

Answer :

Final answer:

The false statement is that if a transversal cuts two lines creating pairs of interior angles on the same side that are complementary, then the lines are parallel. This is incorrect because when a transversal intersects parallel lines, the same side interior angles are supplementary, not complementary.

Explanation:

Transversal lines and parallel lines, understanding of various angles such as corresponding angles, alternate interior angles, and same side interior angles are important. As you stated in your question, if a transversal cuts two lines such that pairs of corresponding angles or alternate interior angles are equal, then the two lines are indeed parallel.

Additionally, if the transversal creates pairs of interior angles on the same side that are supplementary (adding up to 180 degrees), the lines are also parallel.

However, the final statement in your question is false. If a transversal cuts two lines such that pairs of interior angles on the same side are complementary (adding up to 90 degrees), this does not ensure the lines are parallel.

Learn more about Parallel Lines here:

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