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

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.

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

Derrick completed the proof incorrectly. In his proof, he incorrectly stated that angle AKG is congruent to angle BKL instead of angle AKL. This mistake led to an incorrect conclusion that angle AKG is congruent to angle ELK. Therefore, Michael's proof is correct as he correctly identified angle AKG as being congruent to angle AKL before using the Transitive Property to show that angle AKG is congruent to angle ELK.