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5.06 Quiz: Converses of Paraliel Line Properties
Gven .
Which lines, if any, must be parallel based on the given information? Justify your conclusion.
c || d. Converse of the Same-Side Interior Angles Theorem
a . converse of the Alternate Interior Angles Theorem
. Converse of the Corresponding Angles Theorem
not enough information to make a conclusion

Ask by Daniel Bradley. in the United States
Jan 18,2025

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Las líneas c y d son paralelas porque los ángulos correspondientes y son congruentes.

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The Deep Dive

If , then we can conclude that lines c and d must be parallel according to the Converse of the Corresponding Angles Theorem. This theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. So, since and are equal, we can confidently say that lines c and d are parallel!
It’s always good to remember that not all angle relationships guarantee that lines are parallel. For example, even if you find alternate interior angles congruent, that doesn’t apply here directly to your angles 9 and 13 unless they’re in that specific arrangement with the correct transversal. Always check the configuration when applying these theorems!

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