Question

Write a two-column proof of the theorem. What will be your last reason?

If ZRSM = USMU, then PS || LM.

Answer 1

To prove that PS is parallel to LM if ZRSM = USMU, we can use the converse of the Alternate Interior Angles Theorem.

Step-by-step explanation:

To prove that PS is parallel to LM if ZRSM = USMU, we can use the converse of the Alternate Interior Angles Theorem. The theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. In this case, we are given that ZRSM is congruent to USMU, which means that the alternate interior angles are congruent. Therefore, we can conclude that PS is parallel to LM.

Two-Column Proof:

Statements
1. ZRSM = USMU (Given)
2. ∠SRP = ∠UML (Alternate Interior Angles)
3. PS || LM (Converse of Alternate Interior Angles Theorem)

Reasons
1. Given
2. Corresponding angles are congruent
3. If alternate interior angles are congruent, then lines are parallel.