Question

Michael and Derrick each completed a separate proof to show that corresponding angles AKG and ELK are congruent. Who completed the proof incorrectly? Explain. (10 points)



Line AB is parallel to EF, transversal GJ crosses line AB at K and crosses line EF at L.



Michael's Proof



Statement Justification

1. line AB ∥ line EF with transversal segment GJ 1. Given

2. angle AKG is congruent to angle AKL 2. Vertical Angles Theorem

3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem

4. angle AKG is congruent to angle ELK 4. Transitive Property





Derrick's Proof



Statement Justification

1. line AB ∥ line EF with transversal segment GJ 1. Given

2. angle AKG is congruent to angle BKL 2. Vertical Angles Theorem

3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem

4. angle AKG is congruent to angle ELK 4. Transitive Property

Answer 1

Answer:

Michael completed the proof incorrectly.

Step-by-step explanation:

In step 2, Michael incorrectly stated that ∠AKG ≅ ∠AKL due to the vertical angles theorem.

The vertical angles theorem states that when two straight lines intersect, the opposite vertical angles are congruent. In the case of angles AKG and AKL, they are not positioned opposite to each other; rather, they are adjacent. Therefore, they are not congruent by the vertical angles theorem.