Proving Lines Are Parallel
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If two lines are cut by a transversal so that a pair of
corresponding angles are congruent, then the two
lines are parallel.
If two lines are cut by a transversal so that a pair of
alternate interior angles are congruent, then the two
lines are parallel.
If two lines are cut by a transversal so that a pair of
alternate exterior angles are congruent, then the
two lines are parallel.
If two lines are cut by a transversal so that a pair of
same-side interior angles are supplementary, then
the two lines are parallel.
Converse of Corresponding Angles Postulate
Converse of Alternate Interior Angles Theorem
Converse of Alternate Exterior Angles Theorem
Converse of Same-Side Interior Angles Theorem
Given that ∠1 ≅ ∠2 , prove 𝑚 ∥ 𝑛 using the reasons below. Pick the reason that best fits with the statement
provided and write the reason in the blanks provided.
A)
B)
C)
D)
Vertical Angles Theorem
Corresponding Angles Postulate Converse
Given
Transitive Property of Congruence
STATEMENT
1 ∠1 ≅ ∠2)
REASON
1)
2) ∠2 ≅ ∠3
2)
3) ∠1 ≅ ∠3
3)
4) 𝑚 ∥ 𝑛
4)
Given that ∠1 𝑎𝑛𝑑 ∠2 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 , prove 𝑚 ∥ 𝑛 using the statements and reasons below. Pick the
statement or reason that best fits and write it in the blanks provided.
A) ∠2 ≅ ∠3
B) ∠1 𝑎𝑛𝑑 ∠3 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦
C) Alternate Interior Angles Converse
D) Given
STATEMENT
1) ∠1 𝑎𝑛𝑑 ∠2 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦
REASON
1)
2)
2) Linear Pair Postulate
3)
3) Congruent Supplements Theorem
4) 𝑚 ∥ 𝑛
4)
Use the given information for the diagram to determine which value of x would make line p parallel to
line q.
1. 𝑚∠1 = (4𝑥 + 16)°, 𝑚∠8 = (5𝑥 − 12)°
2. 𝑚∠3 = (17𝑥 + 37)°, 𝑚∠5 = (9𝑥 − 13)°
Name the postulate or theorem that proves 𝒍 ∥ 𝒎.
3. ∠8 ≅ ∠6
4. ∠8 ≅ ∠4
5. ∠2 ≅ ∠6
6. ∠7 ≅ ∠5
7. ∠3 ≅ ∠7
8. 𝑚∠2 + 𝑚∠3 = 180°
For the given information, tell which pair of lines must be parallel. Name the postulate or theorem that
supports your answer.
9. 𝑚∠2 = 𝑚∠10
10. 𝑚∠8 + 𝑚∠9 = 180°
11. ∠1 ≅ ∠7
12. 𝑚∠10 = 𝑚∠6
13. ∠11 ≅ ∠5
14. 𝑚∠2 + 𝑚∠5 = 180°
15.
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