Grade 12 Geometry: Parallel Line Proofs
Worksheet focusing on parallel line theorems and proofs, including alternate interior angles, corresponding angles, and consecutive interior angles.
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Grade 12 Geometry: Parallel Line Proofs
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Read each question carefully and provide a clear, logical proof or solution. Show all your work.
1. Given that lines l and m are parallel, and t is a transversal intersecting l and m, prove that alternate interior angles are congruent.
2. Refer to the diagram below where lines p and q are parallel and r is a transversal.
a) Angles A and E are angles.
b) Angles D and F are angles.
c) Angles C and F are angles.
3. Which of the following conditions guarantees that lines a and b are parallel?
∠1 and ∠3 are supplementary
∠2 and ∠4 are congruent
∠1 and ∠4 are congruent
∠1 and ∠2 are complementary
4. In the figure below, if lines j and k are parallel, find the value of x.
5. If two lines are cut by a transversal and consecutive interior angles are congruent, then the lines are parallel.
True
False