Parallel Line Proofs Worksheet
This worksheet focuses on proving lines are parallel using angle relationships formed by transversals, suitable for Grade 11 Geometry students.
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Parallel Line Proofs
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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?
Consecutive interior angles
Same-side exterior angles
Alternate interior angles
Corresponding angles are supplementary
2. To prove two lines are parallel using the Converse of the Alternate Exterior Angles Theorem, what must be true?
Corresponding angles are congruent
Alternate exterior angles are congruent
Consecutive interior angles are congruent
Alternate interior angles are supplementary
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.
True
False
6. The converse of a theorem always states the opposite of the original theorem.
True
False
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.