Given: ∠2 and ∠5 are supplementary

Question

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. _____________(6 points)

Answer 1

Statements Reasons
1. ∠2 and ∠5 are supplementary 1. Given
2. ∠3 and ∠2 are approximately equal 2. Definition of vertical angles
3. ∠3 and ∠5 are supplementary 3. Transitive property of equality (since ∠3 ≈ ∠2 and ∠2 and ∠5 are supplementary)
4. ∠3 and ∠5 are equal 4. Definition of supplementary angles
5. ∠1 and ∠4 are supplementary 5. Transitive property of equality (since ∠2 and ∠5 are supplementary and ∠3 and ∠5 are supplementary)
6. ∠1 and ∠4 are equal 6. Definition of supplementary angles
7. Lines l and m are parallel 7. If two lines are cut by a transversal and the corresponding angles are equal, then the lines are parallel (Alternate Interior Angles Theorem).

Therefore, lines l and m are parallel.