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# . Parallel Lines: What You Need to Prove Them

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Question: If it is given that L is parallel to N, then prove that the measure of angle 2 and the measure of angle 7 add up to 180 degrees by creating a two column proof but you can only use angles 6, 7, and 2 and it gives you the statements, but you have to come up with the reasons. The statements are: L is parallel to N, angles 7 and 6 are supplementary, the measure of angles 7 and 6 add up to 180, angle 6 is congruent to angle 2, the measure of angle 6 is equal to the measure of angle 2, the measure of angles 7 and 2 add up to 180

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Sure! Below you will find a two column proof table. The left column contains the given statement and the right column provides reasons using the properties of the angles you mentioned. | Statements | Reasons | | --- | --- | | L is parallel to N | Given | | Angles 7 and 6 are supplementary | Definition of supplementary angles | | The measure of angles 7 and 6 add up to 180 | Definition of supplementary angles | | Angle 6 is congruent to angle 2 | Alternate interior angles are congruent when lines are parallel | | The measure of angle 6 is equal to the measure of angle 2 | Definition of congruent angles | | The measure of angles 7 and 2 add up to 180 | Substitution property of equivalence – you can replace angle 6 with angle 2 because they are congruent and thus have the same measure | This completes the proof, showing that, if line L is parallel to line N, then the measure of angle 2 and the measure of angle 7 add up to 180 degrees.

Dec. 16, 2023, 7 a.m.

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