Download Parallel Lines Proofs Worksheet

Lesson 2.6: Parallel Lines
Proofs Worksheet
Honors Geometry
Mr. Ferwerda
Name:
1. Without using a protractor, find the measures of all the lettered angles. [Given:
l3
l2
a
e
d
g
l
m
j
i
c
b
f
y
z
α
k
l4
126°
l1
h
l1 // l 2; l 3 // l 4]
n
β
x
w
γ
δ
s
q
o
p
r
l5
157°
u
t
149°
In problems 2 – 6, write complete proofs.
2.
Prove the Alternate Exterior Angles Theorem:
l
1
3
If 2 parallel lines are cut by a transversal, then the
alternate exterior angles are congruent.
m
Given:
l //
Prove:
∠2 ≅ ∠7
7 8
m
Conclusions
5
Justifications
6
2
4
Lesson 2.6: Parallel Lines Proofs Worksheet
3.
page 2
Prove the Same Side Exterior Angles Theorem:
l
1
If 2 parallel lines are cut by a transversal, then the
same side exterior angles are supplementary.
3
5 6
7 8
m
Given:
l //
Prove:
∠1 and ∠7 are supplementary
m
Conclusions
Justifications
m
l
4.
Given:
Prove:
∠1 ≅ ∠2
∠1 ≅ ∠4
l //
m
Conclusions
3
2
1
Justifications
4
2
4
Lesson 2.6: Parallel Lines Proofs Worksheet
5.
Given:
l //
Prove:
∠4 ≅ ∠10
m;
//
m
n
page 3
1 4
2 3
l
Conclusions
6.
9 12
5 8
6 7
m
10 11
n
Justifications
Prove the Transitivity of Parallels Theorem:
If 2 lines are parallel to the same line, then those
lines are parallel to each other.
1
a
2
b
[Hint: use the numbered angles!]
Given:
a
//
b;
Prove:
a
//
c
b
//
Conclusions
c
c
Justifications
3