Question

Which of the following correctly justifies statement 4 of the two-column proof?

Lines JK and LM are intersected by transversal JL; the intersection of JK and JL creates angles 2, 4, 3, and 1 clockwise beginning at the top right; the intersection of LM and JL creates angles 6, 8, 7, and 5 clockwise beginning at the top right.

Given: line JK is parallel to line LM

Prove: ∠3 ≅ ∠6

Statement Justification
1. line JK is parallel to line LM 1. Given
2. ∠7 ≅ ∠6 2.
3. ∠3 ≅ ∠7 3.
4. ∠3 ≅ ∠6 4.
Corresponding Angles Theorem
Vertical Angles Theorem
Substitution Property of Equality
Transitive Property of Equality

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct justification for statement 4 is the Transitive Property of Equality. This property states that if two things are equal to the same thing, then they are equal to each other. In this case, ∠3 is equal to ∠7 (justified by statement 3) and ∠7 is equal to ∠6 (justified by statement 2), therefore ∠3 is equal to ∠6.