# Parallel And Perpendicular Lines Worksheet Page 12

Standardized
Use an Auxiliary Line
Example
Example
2
2
Test Practice
Grid-In Test Item
What is the measure of
GHI?
G
B
A
E
40
˚
H
F
70
˚
C
D
I
You need to find m GHI. Be sure to identify it correctly on the figure.
Solve the Test Item
G
A
B
E
Draw JK through H parallel to AB and CD.
40
˚
EHK
AEH
H
J
Alternate Interior Angles Theorem
K
F
70
˚
Test-Taking Tip
m EHK
m AEH
Definition of congruent angles
C
D
I
Make a Drawing If you
m EHK
40
Substitution
are allowed to write in
FHK
CFH
Alternate Interior Angles Theorem
1 1 0
m FHK
m CFH
Definition of congruent angles
/
/
organized. Do not make
m FHK
70
Substitution
.
.
.
.
0
0
0
1
1
1
1
m GHI
m EHK
m FHK
2
2
2
2
3
3
3
3
40
70
or 110
m EHK
40, m FHK
70
4
4
4
4
5
5
5
5
Write each digit of 110 in a column of the grid. Then
6
6
6
6
7
7
7
7
shade in the corresponding bubble in each column.
8
8
8
8
9
9
9
9
ALGEBRA AND ANGLE MEASURES
Angles formed by two parallel lines
and a transversal can be used to find unknown values.
Find Values of Variables
Example
Example
3
3
ALGEBRA
If m 1
3x
40, m 2
2(y
10),
and m 3
70, find x and y.
2x
1
F
• Find x.
Since FG EH,
1
3 by the
3
E
G
Corresponding Angles Postulate.
2
m 1
m 3
Definition of congruent angles
4
H
3x
40
2x
70
Substitution
x
30
Subtract 2x and 40 from each side.
• Find y.
Since FE
GH,
1
2 by the Alternate Exterior Angles Theorem.
m 1
m 2
Definition of congruent angles
3x
40
2(y
10)
Substitution
3(30)
40
2(y
10)
x
30
130
2y
20
Simplify.
150
2y
75
y
Divide each side by 2.
Lesson 3-2 Angles and Parallel Lines 135