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

Answer: Derrick

Step-by-step explanation:

$Vertical Angle Theorem:- \\Vertical angle theorem or vertically opposite angles theorem states that two oppositevertical angles formed where two line intersect each other are always equal.$

$Solution: Michael used the incorrect vertical angle theorem in his statement. From figure \angle A K O T \cong L B K L(\because \text { Vertical angle theorem})$

$Therefore, Derrick gave the correct proof and so Michael's proof is incorrect$