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

completed the proof incorrectly? Explain.

Michael is the one whose proof was completed incorrectly.

Step-by-step explanation:

The complete Question, the image of the angles being analysed and their respective proofs are presented in the attached image.

Michael proves that

1) Line AB is parallel to line EF with a transversal line GF (Given)

2) Angle AKG = Angle AKL (Vertically opposite angles are equal)

3) Angle BKL = Angle ELK (Alternate angles are equal)

4) Angle AKG = Angle ELK (Transitive property)

Derrick's Proof

1) Line AB is parallel to line EF with a transversal line GF (Given)

2) Angle AKG = Angle BKL (Vertically opposite angles are equal)

3) Angle BKL = Angle ELK (Alternate angles are equal)

4) Angle AKG = Angle ELK (Transitive property)

Derrick's Proof, from the first statement to the last, is entirely, mathematically correct and he establishes the transitive property that

Angle AKG = Angle BKL = Angle ELK

Hence, Angle AKG = Angle ELK

But Michael makes his own mistake on the second statement.

He says, Angle AKG = Angle AKL (Vertically opposite angles are equal) which is not mathematically true.

Angle AKG and Angle AKL are supplementary angles that sum up to 180° because they both make up the angle on the straight line GJ at the point K.

Furthermore, this makes his transitive claim not correct, because at the end of the day, he will obtain

Angle AKG = Angle AKL

Angle BKL = Angle ELK

So, Angle AKG ≠ Angle ELK with this proof.

It's either he made the mathematical error or he actually made a typographical error and wrote angle AKL in that 2nd statement instead of angle BKL because the rest of his proof seem to be on point.

Either ways, Michael's proof is the proof that is completed incorrectly.

Hope this Helps!!!