3.3 Prove Lines are Parallel
Name __________________________________ Class Period _________
Is it possible to prove that lines p and q are parallel? If so, state the postulate or theorem that you would use.
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Find the value of x that makes m ∥ n.
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In Problems 10 – 12, circle the word that best completes the statement.
10. If two lines are cut by a transversal so the alternate interior angles are ( congruent,
complementary), then the lines are parallel.
11. If two lines are cut by a transversal so the consecutive interior angles are ( congruent,
complementary), then the lines are parallel.
12. If two lines are cut by a transversal so the corresponding angles are ( congruent,
complementary), then the lines are parallel.
supplementary,
supplementary,
supplementary,
13. A garden has five rows of vegetables. Each row is parallel to the row immediately
next to it. EXPLAIN why the first row is parallel to the last row.
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In Problems 14 – 18, complete the two column proof.
Given: n ∥ m, 1  2
2x-Given, 1x-Alternate Interior Angles Theorem,
Prove: p ∥ r
1x-Alternate Interior Angles Converse,
Statements
n ∥m
Reasons
1x-Transitive Property
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1  3
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1  2
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2  3
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p ∥r
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19. Railroad Tracks- Two sets of railroad tracks intersect as shown. How do you
know that line n is parallel to line m ?
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