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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: Segment JK is parallel to Segment LM

Prove: [tex]\angle 2 \cong \angle 7[/tex]

| Statement | Justification |
|-----------------------------------|------------------------------------|
| 1. Segment JK is parallel to Segment LM | 1. Given |
| 2. [tex]\angle 6 \cong \angle 7[/tex] | 2. Corresponding Angles Postulate |
| 3. [tex]\angle 2 \cong \angle 6[/tex] | 3. Corresponding Angles Postulate |
| 4. [tex]\angle 2 \cong \angle 7[/tex] | 4. Transitive Property of Congruence |

Answer :

Final answer:

The justification for statement 4 of the proof '∠2 ≅ ∠7' is based on the Transitive Property of Equality which states that if ∠2 ≅ ∠6 and ∠6 ≅ ∠7, then ∠2 should be congruent to ∠7.

Explanation:

The

justification

for statement number 4 in this two-column proof, namely '∠2 ≅ ∠7', is based on the

Transitive Property

of Equality. In the context of geometry, this principle states that if one angle is congruent to a second angle and the second angle is congruent to a third angle, then the first angle is congruent to third. To apply this in the case of the given proof, since it was previously established that '∠2 ≅ ∠6' (statement 3) and '∠6 ≅ ∠7' (statement 2), we can infer that '∠2 ≅ ∠7'. This step ‐by ‐step approach assists in understanding the logical reasoning behind geometric proofs, reinforcing the importance of foundational principles such as the Transitive Property.

Learn more about Transitive Property here:

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