Download Worksheet on Parallel Lines and Transversals

Geometry
Name
3.1-3.3 Review #2
Date
Hour
I can identify relationships between lines. (parallel, perpendicular, skew) (#1-5)
I can define parallel lines (#6-9)
I can determine angle pair names when two lines are cut by a transversal. (#10)
I can determine and justify angle measures when parallel lines are cut by a transversal. (#11-24)
I can prove theorems about parallel lines and the resulting angle pair relationships. (#25-28)
alternate exterior angles
alternate interior angles
corresponding angles
consecutive interior angles
perpendicular bisector
perpendicular lines
parallel lines
transversal
skew lines
parallel planes
In #1-5, complete the sentences with the vocabulary work from the list above.
1) Angles on opposite sides of a transversal and between the lines it intersects are
2) Lines that do not intersect and are in different planes are
3) A(n)
.
.
is a line that intersects two coplanar lines at two different points.
4) Angles on the same side of a transversal and in between the lines it intersects are
5) Two lines that intersect at a right angle are
In #6-9, identify each of the following.
6) a pair of skew segments
7) a pair of parallel segments
8) a pair of perpendicular segments
9) a pair of parallel planes
10) Define Parallel Lines:
____________________________________________________________________________________
____________________________________________________________________________________
11) True or False: If two lines do not intersect, then they are parallel.
12) Determine if each picture shows parallel lines.
.
.
13) Draw a diagram that represents j k .
2 3
1 4
5
8
6
7
13 14
16 15
9 10
12 11
14) Refer to the above figure and identify the special angle pair name.
a) 3 and 13 ______________________________________________________
b) 8 and 10 _____________________________________________________
c) 11 and 15 ____________________________________________________
d) 8 and 6 ____________________________________________________
e) 1 and 6 _____________________________________________________
f) 6 and 10 _____________________________________________________
g) 14 and 15 _____________________________________________________
15)
m1 = 3x - 17
m2 = x + 1
x = ________
16)
1
3
4
m3 = 20k + 11
m4 = 8k + 1
k = _________
17)
m1 = 95 + 7h
m2 = 55 – h
h = ________
3 1
2
4
18)
m3 = 5k + 12
m4 = 7k - 16
k = _________
2
1 2
5 6
3 4
7 8
11 12
15 16
9 10
13 14
Let m1 = 115 and m12 = 110. Find the measure of each indicated angle.
19) m9 = ______
20) m4 = ______
21) m10 = ______
22) m11 = ______
23) m8 = ______
24) m5 = ______
25) m3 = ______
26) m14 = ______
27)
To solve for x in the diagram below,
John used the equation 4x +10 = 42.
Write out the theorem or postulate
that allows him to do so.
21.
28) To solve for x in the diagram below,
Jenna used the equation 4x – 10+50 = 180.
Write out the theorem or postulate that
allows her to do so.
(4x +10)°
a
h
k
b
42°
Complete the proofs.
29) Given: j k
Prove: 1 and 7 are supplementary
Statements
Reasons
(4x – 10)°
50°
30) Complete the proof of the Consecutive Interior Angles Theorem (you cannot use the theorem
anywhere in the proof!).
31)
Given: a b and h j
Prove: 3  9
Statements
Reasons
1. a b and h j
1.
1  3
2.
3. 1  9
3.
2.
4.
32)
3  9
4.