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. ∠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.
Statements Reasons
1. ∠2 and ∠5 are supplementary 1. Given
2. ∠3 and ∠2 are approximately equal 2. Corresponding angles formed by parallel lines and a transversal are congruent
3. ∠3 and ∠5 are supplementary 3. ∠2 and ∠5 are supplementary, and ∠3 is congruent to ∠2
4. ∠3 and ∠5 are congruent 4. Supplementary angles that are congruent are angles of parallel lines
5. ∠4 and ∠6 are congruent 5. Corresponding angles formed by parallel lines and a transversal are congruent
6. ∠5 and ∠7 are congruent 6. Corresponding angles formed by parallel lines and a transversal are congruent
7. ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 are congruent 7. ∠3 is congruent to ∠2 (Step 3), ∠4 is congruent to ∠6 (Step 5), and ∠5 is congruent to ∠7 (Step 6)
8. All six angles are congruent 8. ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 are all congruent
9. l is parallel to m 9. If all corresponding angles are congruent, then the lines are parallel