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.
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. _____________
1 answer