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. _____________
Statements Reasons
1. ∠1 is congruent to ∠5 1. Vertical angles are congruent.
2. ∠3 is congruent to ∠2 2. Alternate interior angles are congruent.
3. ∠3 and ∠5 are supplementary 3. Given information.
4. ∠1 and ∠2 are congruent 4. Transitive property of congruence.
5. l is parallel to m 5. If two lines are intersected by a transversal and corresponding angles are congruent, then the lines are parallel.
Statements Reasons
1. ∠2 and ∠5 are supplementary 1. Given
2. ∠3 + ∠5 = 180° 2. Definition of supplementary angles
3. ∠3 + ∠2 = 180° 3. Substitution property of equality
4. ∠3 + ∠2 = ∠6 + ∠5 4. Corresponding angles are congruent (alternate interior angles formed by the transversal)
5. ∠6 + ∠5 = ∠5 + ∠6 5. Commutative property of addition
6. ∠3 + ∠2 = ∠5 + ∠6 6. Transitive property of equality
7. ∠3 + ∠2 = ∠2 + ∠5 7. Commutative property of addition
8. ∠3 = ∠5 8. Subtraction property of equality
9. l is parallel to m 9. If alternate interior angles are congruent, then the lines cut by the transversal are parallel