EXPLAIN 1 Proving That Alternate Interior Angles Are Congruent Read Explain 1 & Explain2 and complete Your Turn #1 (adapted from Lesson 4.2). Show all your work. Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure. Example: 2325 Example Complete the proof by writing the missing reasons. Choose from the following reasons. You may use a reason more than once. Refer to the reason bank below. Given: p q (line p parallel to line q) Prove: m23 = m25 Two-Column Proof of the Alternate Interior Angles Theorem At 1/2 P 4/3 5 6 b 8/7 Statements Reasons 1. pl q 1. 2. 23 and 26 are supplementary. 2. 3. m23+m26 = 180. 3. 4. 25 and 26 are a linear pair. 4. 5. 25 and 26 are supplementary. 5. 6. m25+m26 = 180. 6. 7. m23+m26 = m25+ m26 7. 8. m23m25 8. Reason Bank: Same-Side Interior Angles Postulate Linear Pair Theorem Subtraction Property of Equality Substitution Property of Equality Definition of Supplementary Angles Given