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

Question

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: ∠2 ≅ ∠7

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

Answer 1

To justify statement 4, which asserts that ∠2 ≅ ∠7, we can use the Transitive Property of Equality.

Here's the reasoning:

1. From statement 2, we know ∠6 ≅ ∠7 based on the property of parallel lines cut by a transversal (specifically corresponding angles).
2. From statement 3, we have ∠2 ≅ ∠6 based on a similar reasoning (∠2 and ∠6 are also corresponding angles created by the transversal JL intersecting the parallel lines JK and LM).

Using the Transitive Property of Equality: if ∠2 ≅ ∠6 and ∠6 ≅ ∠7, then it follows that ∠2 ≅ ∠7.

Thus, the correct justification for statement 4 is:

4. Transitive Property of Equality.