Given: <2 and <5 are supplementary
Prove: I || m
Statements
1.
2. <3 ≈ <2
3. <3 and L 5 are supplementary
4.
Reasons
1.
2.
3.
4.
Statements
1. Given: <2 and <5 are supplementary
2. Given: <3 ≈ <2
3. Given: <3 and <5 are supplementary
4. If two angles are congruent to the same angle or to congruent angles, then the two angles are congruent (angle congruence is transitive)
Reasons
1. -
2. -
3. -
4. Transitive Property of Angle Congruence
Therefore, based on the transitive property of angle congruence, <3 and <5 are congruent. Given that <3 and <5 are supplementary, this implies that they are two adjacent angles. By the definition of parallel lines, if two adjacent angles are supplementary, then the lines that contain those angles are parallel. Therefore, it can be concluded that line I is parallel to line m.