Question 1: Jaymie wants to construct congruent angles with a compass and straightedge, while Annie wants to construct congruent segments with a compass and straightedge. Describe the similarities and differences between their construction steps.

Question 2: Describe at least two similarities between constructing a perpendicular line through a point on a line and constructing a perpendicular through a point off a line.

Question 3: 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