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

Given: line JK is parallel to line LM
Prove: ∠3≅∠6∠3≅∠6
Statement Justification
1. line JK is parallel to line LM | 1. Given
2. ∠7≅∠6∠7≅∠6 | 2. Definition of angles formed by parallel lines and a transversal
3. ∠3≅∠7∠3≅∠7 | 3. Transitive property of angle congruence
4. ∠3≅∠6∠3≅∠6 | 4. Transitive property of angle congruence

User Miccet
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Final answer:

The correct justification for statement 4, which asserts that angle 3 is congruent to angle 6, is the Transitive Property of Angle Congruence. This conclusion is reached by combining the facts from earlier statements that establish angle 7 is congruent to both angle 6 and angle 3.

Step-by-step explanation:

The question is asking for the correct justification for statement 4 in a two-column geometry proof. Statement 4 asserts that angle 3 is congruent to angle 6 (∠3≅∠6). Given that line JK is parallel to line LM, we have previously established in statement 2 that angle 7 is congruent to angle 6 (∠7≅∠6) based on the Alternate Interior Angles Theorem, which is applicable because the angles are formed by parallel lines and a transversal. In statement 3, we established that angle 3 is congruent to angle 7 (∠3≅∠7) through the Transitive Property of Angle Congruence, which tells us that if two angles are both congruent to a third angle, then they are congruent to each other. To justify statement 4, we combine the facts from statements 2 and 3 and apply the Transitive Property once more (∠3≅∠7 and ∠7≅∠6, therefore ∠3≅∠6). Therefore, the correct justification for statement 4 is the Transitive Property of Angle Congruence.

User Jenglert
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