2:19 PM Wed Feb 19 \( 21 \% \) mylabschool.pearson.com ChatGP \( { }^{-} \) Max Headro... Encore: The... The Mystery... K! Kahoot! parallel lines... Geometry Period 11 Mckennah Person 02/19/25 2:19 PM This quiz: 23 point(s) \( \equiv \) Quiz: parallel lines chapter quiz Question 2 of 23 possible This question: 1 Submit quiz point(s) possible Question list Question 1 Question 2 Question 3 Question 4 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Use the given information to determine which lines, if any, in the figure to the right are parallel. Justify each conclusion with a theorem or postulate. \( \angle 2 \) is supplementary to \( \angle 3 \). Fill in the blanks below. Because it is given that \( \angle 2 \) is supplementary to \( \angle 3 \), a || b by the Converse of the Alternate Interior Angles Theorem. Converse of the Corresponding Angles Theorem. Converse of the Alternate Exterior Angles Theorem. Converse of the Same-Side Interior Angles Postulate.

To determine which lines are parallel based on the given information that \( \angle 2 \) is supplementary to \( \angle 3 \), we can analyze the situation using the properties of angles formed by a transversal intersecting two lines. ### Step-by-Step Solution: 1. **Understanding Supplementary Angles**: - Two angles are supplementary if their measures add up to \( 180^\circ \). In this case, since \( \angle 2 \) and \( \angle 3 \) are supplementary, we have: \[ \angle 2 + \angle 3 = 180^\circ \] 2. **Identifying the Relationship**: - The relationship between \( \angle 2 \) and \( \angle 3 \) is crucial. If these angles are formed by a transversal intersecting two lines, we can apply the appropriate theorem or postulate to determine if the lines are parallel. 3. **Applying the Theorems**: - The relevant theorem here is the **Converse of the Same-Side Interior Angles Postulate**, which states that if a transversal intersects two lines and the same-side interior angles are supplementary, then the two lines are parallel. 4. **Conclusion**: - Since \( \angle 2 \) is supplementary to \( \angle 3 \), we conclude that the lines are parallel. ### Fill in the Blank: Because it is given that \( \angle 2 \) is supplementary to \( \angle 3 \), we can conclude that lines \( a \) and \( b \) are parallel by the **Converse of the Same-Side Interior Angles Postulate**. ### Final Answer: **Converse of the Same-Side Interior Angles Postulate.**