Parallel Line Proofs Worksheet

Parallel Line Proofs

Read each question carefully and provide clear, logical proofs or answers. Show all your work.

1. If two parallel lines are cut by a transversal, which pair of angles are congruent?

2. To prove two lines are parallel using the Converse of the Alternate Exterior Angles Theorem, what must be true?

3. If two lines are cut by a transversal and the   angles are supplementary, then the lines are parallel.

4. The   Postulate states that if two parallel lines are cut by a transversal, then the corresponding angles are congruent.

5. If alternate interior angles are congruent, then the lines are parallel.

6. The converse of a theorem always states the opposite of the original theorem.

7. Given two lines 'a' and 'b' cut by a transversal 't'. If ∠1 and ∠2 are consecutive interior angles and m∠1 + m∠2 = 180°, explain why lines 'a' and 'b' must be parallel.

8. In the diagram below, lines 'm' and 'n' are intersected by transversal 'p'. If ∠3 and ∠6 are alternate exterior angles and m∠3 = 75°, what must m∠6 be for lines 'm' and 'n' to be parallel? Justify your answer.

9. Write a two-column proof to prove that if two lines are perpendicular to the same line, then they are parallel to each other.