Given: ∠2 and ∠5 are supplementary
Prove: l is parallel to m
Two horizontal lines, l and m, appear to be parallel and are cut by a transversal, creating 8 angles.
Line l is above line m.
Angle 1 is above line l and to the left of the transversal.
Angle 2 is above line l and to the right of the transversal.
Angle 3 is below line l and to the left of the transversal.
Angle 4 is below line l and to the right of the transversal.
Angle 5 is above line m and to the left of the transversal.
Angle 6 is above line m and to the right of the transversal.
Angle 7 is below line m and to the left of the transversal.
Angle 8 is below line m and to the right of the transversal.
Statements Reasons
1. _____________ 1. _____________
2. ∠ 3 approximately equal to∠ 2 2. _____________
3. ∠ 3 and ∠ 5 are supplementary 3. _____________
4. _____________ 4. _____________
Statements Reasons
1. ∠2 and ∠5 are supplementary. 1. Given
2. ∠3 and ∠5 are supplementary. 2. ∠3 is vertically opposite to ∠2
3. ∠3 and ∠5 are congruent. 3. If two angles are supplementary to the same angle, then they are congruent to each other.
4. ∠3 is congruent to ∠5. 4. If two angles are congruent to the same angle, then they are congruent to each other.
5. l is parallel to m. 5. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
Statements Reasons
1. Angle 2 and Angle 5 are supplementary. 1. Given (Given: ∠2 and ∠5 are supplementary)
2. Angle 3 is vertically opposite to Angle 2. 2. Definition of vertical angles
3. Angle 3 and Angle 5 are supplementary. 3. Transitive property of equality (If Angle A is congruent to Angle B, and Angle B is congruent to Angle C, then Angle A is congruent to Angle C)
4. Angle 3 and Angle 5 are supplementary, and Angle 5 and Angle 2 are supplementary. 4. Transitive property (If A = B, and B = C, then A = C)
5. l is parallel to m. 5. If two angles are supplementary to the same angle (Angle 5 in this case), then the two angles are congruent, and the lines they are on are parallel (Corresponding Angles Postulate).