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Geometry
Properties of Parallel Lines
1 4
2 3
5 8
6 7
9 12
10 11
13 16
14 15
Complete.
1) If m∠2 = 85, then m∠6 = _____ and m∠7 = _____
2) If m∠8 = 83, then m∠16 = _____ and m∠10 = _____
3) If m∠9 = 105, then m∠10 = _____ and m∠16 = _____
4) If m∠15 = 96, then m∠8 = _____ and m∠1 = _____
Identify each pair of angles in exercises 5-8 as vertical, corresponding, alternate interior, or same-side interior.
5) ∠14 and ∠8
6) ∠9 and ∠13
7) ∠11 and ∠16
8) ∠1 and ∠3
9) If two parallel lines are cut by a transversal, then corresponding angles are _______________________.
10) If two parallel lines are cut by a transversal, then alternate interior angles are _______________________.
11) If two parallel lines are cut by a transversal, then same-side interior angles are _______________________.
.
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Complete a two-column proof.
A
12)
Given: DE BC ; ∠1 ≅ ∠3
Prove: ∠2 ≅ ∠3
D
B
1
3
E
2
C
Complete a two-column proof.
13)
Given: a b
a
3
Prove: ∠1 ≅ ∠3
b
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Answer Key
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
85, 95
83, 83
75, 75
84, 96
Alternate Interior Angles
Corresponding Angles
Same –Side Interior Angles
Vertical Angles
Congruent
Congruent
Supplementary
DE BC ; ∠1 ≅ ∠3 .......... Given
12) ∠1 ≅ ∠2 .......... If two parallel lines are cut by a transversal, then corresponding angles are congruent
∠2 ≅ ∠3 .......... Substitution
13)
a b .......... Given
∠1 ≅ ∠2 .......... If lines are parallel, then corresponding angles are congruent
∠2 ≅ ∠3 .......... Vertical angles are congruent
∠1 ≅ ∠3 .......... Transitive Property of Congruence
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