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: JK ∥ LM
Prove: ∠2 ≅ ∠7

A. Corresponding Angles Theorem
B. Transitive Property of Equality
C. Vertical Angles Theorem
D. Substitution Property of Equality

Question

09-11-2023
Mathematics

High School

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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: JK ∥ LM
Prove: ∠2 ≅ ∠7

A. Corresponding Angles Theorem
B. Transitive Property of Equality
C. Vertical Angles Theorem
D. Substitution Property of Equality

Answer :

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sabanasatik06 sabanasatik06 · Answer 1 · 2024-05-12T20:26:04-04:00

Final answer:

The correct theorem to justify that angle 2 is congruent to angle 7 when lines JK and LM are intersected by transversal JL is the Corresponding Angles Theorem.

Explanation:

The student has described a scenario where lines JK and LM are intersected by transversal JL, creating angles labeled 1 through 8. Given that lines JK and LM are parallel (JK ∥ LM), and we are to prove that ∠ 2 is congruent to ∠ 7 (∠ 2 ≅ ∠ 7), we need to determine which theorem justifies that ∠ 2 is congruent to ∠ 7 based on the described intersecting lines and angles.

The correct justification for statement 4, which asserts that ∠ 2 is congruent to ∠ 7, is the Corresponding Angles Theorem. This theorem states that when two parallel lines are cut by a transversal, the corresponding angles are congruent. In this case, ∠ 2 and ∠ 7 are corresponding angles because they are in the same relative position at each intersection where the transversal (JL) cuts the parallel lines (JK and LM).