Grade 9 Math: Parallel Line Proofs Worksheet
A worksheet for Grade 9 students focusing on understanding and proving theorems related to parallel lines cut by a transversal.
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Standards
Topics
Parallel Line Proofs
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Read each question carefully and provide a complete answer. Show all your work for proofs.
1. In the diagram below, lines 'a' and 'b' are parallel, and 't' is a transversal. Identify the relationship between the following pairs of angles:
a) ∠1 and ∠5:
b) ∠3 and ∠6:
c) ∠4 and ∠5:
d) ∠2 and ∠7:
2. State whether each statement is True or False.
a) If two parallel lines are cut by a transversal, then alternate interior angles are supplementary.
True
False
b) Corresponding angles are always congruent when two lines are intersected by a transversal.
True
False
3. Given: Line m || Line n, and 't' is a transversal. Prove: Alternate exterior angles are congruent.
4. If two lines are cut by a transversal such that consecutive interior angles are supplementary, then the lines are:
Perpendicular
Parallel
Intersecting but not perpendicular
Skew
5. In the figure below, if ∠1 = 110°, what is the measure of ∠8? Justify your answer with a theorem.