Note: Your teacher will grade your response to ensure you receive proper credit for your answers.
Complete the two-column proof.
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. _____________(6 points)
Statements Reasons
1. ∠2 and ∠5 are supplementary 1. Given
2. ∠2 + ∠5 = 180° 2. Definition of supplementary angles
3. ∠3 + ∠5 = 180° 3. ∠3 and ∠5 are supplementary (from statement 1)
4. ∠3 + ∠5 = ∠2 + ∠5 4. Transitive property of equality
5. ∠3 = ∠2 5. Subtraction property of equality (subtracting ∠5 from both sides)
6. l is parallel to m 6. If a pair of alternate interior angles are congruent, then the lines are parallel