Question

1. Write a two-column proof for the following conjecture. You may not need to use all of the rows of the two-column table provided below. You may also add additional rows if needed.
Given:

Prove: and are supplementary.
and are supplementary.

Answer:
Statement Reason
1. 1.
2. 2.
3. 3.
4. 4.
5. 5.
6. 6.
7. 7.

Answer 1

Answer:

Statement — Reason

1. l ∥ m — Given.
2. ∠1 ≅ ∠3 — If two parallel lines are cut by a transversal, corresponding angles are congruent.
3. ∠2 ≅ ∠4 — If two parallel lines are cut by a transversal, corresponding angles are congruent.
4. ∠3 and ∠4 form a linear pair — Definition of a linear pair (they are adjacent and lie on a straight line).
5. ∠3 and ∠4 are supplementary — Linear Pair Postulate.
6. m∠1 + m∠2 = m∠3 + m∠4 — Congruent angles have equal measures; substitute m∠1 for m∠3 and m∠2 for m∠4.
7. m∠1 + m∠2 = 180°, so ∠1 and ∠2 are supplementary; and from (5) ∠3 and ∠4 are supplementary — From (5) and (6) (substitution), therefore both pairs are supplementary. Q.E.D.