CHAPTER 4: BASIC ANGLE RELATIONSHIPS
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Name
Lab: Discovering Angles from Parallel Lines
Identifying Lines, Angles and Relationships
Angles within Parallel Lines
Proving Parallel Lines
Chapter Review
Chapter TEST
Name ___________________________________
Complete?
Score ____/10
October/November
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Geometry
Documents on the
Calculator
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#1 Lab:
#2 Identifying
Discovering Angles Lines, Angles and
from Parallel Lines Relationships
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#3 Angles within
Parallel Lines
#4 Proving Parallel
Lines
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#4 Proving Parallel Chapter 4 Test!
Lines
#5 Chapter Review
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Name ____________________________________
NR Geometry
Lab: Discovering Angles from Parallel Lines
Chp 4 Wksht #1
What you will need: Your TI-Nspire, this sheet, and the lab file sent to your calculator.
**Reminder** to un-do anything, click ctrl, esc
1. Open the file Parallel_Lines_And_Transversals
2. On page 1.2, you will see two parallel lines cut by a transversal.
Be sure to add the definitions to your dictionary
Parallel Lines: Two lines having the same slope, they will never intersect.
Transversal: A line intersecting a line or lines to create a group of angles.
3. Put a point on the other side FA , by going to the Point-On Function (menu,4:Points and Lines,2:Point On)
a.) Select the line and then click the point on the line.
b.) Label it C by pressing shift and the letter C
4. Staying in the point on function (the top left of your screen should still have its icon), repeat the process and
put point E on the other side of line JB
a.) Press escape to exit the point-on function.
5. Staying in the point on function (the top left of your screen should still have its icon), repeat the process and
put point G on the end of line DB
a.) Press escape to exit the point-on function.
6. Measure the following angles (menu,6:Measurement, 4:Angle). Select the letters for the angle you wish to
measure. Remember, you can move any of the measurements by moving the mouse so an open hand is over it,
closing the open hand and then relocating it where you desire.
a.)Round all of your measurements to the nearest whole number by hovering your mouse over the
measurement and clicking the subtract button.
1. mDAF 
2. mDAC 
3. mCAB 
4. mFAB 
5. mABJ 
6. mABE 
7. mEBG 
8. mJBG 
7. Grab point D (hover your mouse over the point until an open hand appears, close the hand by holding down
on the center of the touchpad) and move it anywhere. Record the new angle measures.
1. mDAF 
2. mDAC 
3. mCAB 
4. mFAB 
5. mABJ 
6. mABE 
7. mEBG 
8. mJBG 
8. What do you notice about the measurements?
9.
Also called co-interior
angles
Name the relationship for each pair of angles.
a.) DAF and ABJ
b.) DAF and EBG
c.) DAC and JBG
d.) DAC and ABE
e.) CAB and ABJ
f.) EBA and FAB
g.) CAB and EBA
h.) FAB and JBA
10. When two parallel lines are cut by a transversal, what can you conclude about the relationship of the
following types of angles?
a.) Alternate Interior Angles are ___________________
b.) Alternate Exterior Angles are __________________
c.) Corresponding Angles are _____________________
d.) Same-side/Co-interior angles are __________________
11. Using the theorems above, solve for x in the following examples.
a.)
b.)
3x
x
x+10
x+10
c.) Find the measure of angle 3
d.) Find the measure of all the missing angles
3
4x
x
77o
45o
Name ____________________________________
NR Geometry
1. Solve the following.
a) x = ________
y = ________
b) x = ________ y = ________
c) x = ________ y = ________
3x - 5
x
67°
Identifying Lines, Angles and Relationships
Chp 4 Wksht #2
y
y
y
5x - 15
127°
2. 5 and 3 are vertical angles.
T or F
3. 1 and 5 are a linear pair.
T or F
4. 4 and 3 are adjacent angles.
T or F
5. 4 and 1 are vertical angles.
T or F
6. 3 and 4 are a linear pair.
T or F
2
3
1
4
5
7. If A and B are supplements and mA = 150, what is mB? ___________
8. If A and B are complements and mA = 27, what is mB? ___________
9. If A and B are vertical angles and mA = 36, what is mB? ___________
10. If A and B are a linear pair and mA = 2x + 8 and mB = 3x + 2, what is the value of x? x = _______
11. If A and B are vertical angles and mA = 7x -5 and mB = 4x + 10, what is the value of x? x = _______
12. Provide the name of the following relationships.
a) 1 & 6 ________________ b) 2 & 7 ________________
c) 16 & 14 ________________
d) 14 & 11 _______________
1
3
h) 1 & 2 ________________
i) 13 & 12 ________________
j) 16 & 9 ________________
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13
2
4
12
e) 1 & 7 ________________ f) 6 & 5 ________________
g) 15 & 10 ________________
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16
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8
11
10
13. Find the measure of the angle and give a reason for knowing it.
(measure)
(reason)
a) m1 = ___________ _______________________
b) m2 = ___________ _______________________
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2
c) m3 = ___________ _______________________
3
d) m4 = ___________ _______________________
e) m5 = ___________ _______________________
4
110°
1
50°
14. Find the measure of the angle.
4
a) m1 = ___________ b) m2 = ___________
2
c) m3 = ___________ d) m4 = ___________
1
e) m5 = ___________ f) m6 = ___________
83°
3
5
6
15. Circle (T)rue or (F)alse.
a) 1  4
T or F
b) 6  16
T or F
c) 3  5
T or F
d) 4  5
T or F
e) 2  10
T or F
f) 9  15
T or F
g) 12  14 T or F
h) 9  11
T or F
1
3
9
4
5
i) m11 + m15 = 180 T or F
j) m1 + m8 = 180
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12
6
8
10
11
13
7
16
T or F
16. Solve for the unknown values.
a) x = ___________
b) x = ___________
c) x = ___________
8x - 4
3x + 16
2x + 13
5x - 10
3x + 17
160°
d) x = ___________
e) x = ___________
f) x = ___________
118°
109°
4x + 32
5x - 7
172°
3x + 16
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Name ____________________________________
NR Geometry
Angles within Parallel Lines
Chp 4 Wksht #3
1. Solve the following.
a) if m7 = 100, find m3 = _______
b) if m7 = 95, find m6 = _______
c) if m1 = 120, find m5 = _______
d) if m4 = 20, find m7 = _______
e) if m3 = 140, find m5 = _______
f) if m4 = 30, find m1 = _______
g) if m4 = 40, find m2 = _______
h) if m3 = 125, find m8 = _______
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3
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6
5
7
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i) if m1 + m5 = 234, find m6 = _______
2. Solve the following.
a) m 1 = ____________
b) m 2 = ____________
c) m 3 = ____________
d) m 4 = ____________
e) m 5 = ____________
f) m 6 = ____________
3. Solve the following.
a)
x = ________
115°
6
32°
1
2
3
5
4
b)
x = ________
6y
4x - 5
y = ________
y = ________
3y + 1
9x + 12
13y - 10
3x + 11
4. Solve
a) m 6 = _______
131°
b) m 7 = _______
2
5. Solve
a) m 7 = _______
58°
c) m 4 = _______
5
b) m 5 = _______
6
c) m 6 = _______
3
d) m 2 = _______
26°
6
d) m 4 = _______
7
4
e) m 5 = _______
47°
4
5
7
8
e) m 8 = _______
8
f) m 8 = _______
6. Solve
a) m 5 = _______
A
c) m 4 = _______
d) m 6 = _______
e) m 2 = _______
B
42°
b) m 1 = _______
7. Solve
a) m 3 = _______
54°
D
6
C
b) m 5 = _______
5
1
4
18°
48°
2
c) m 1 = _______
d) m 4 = _______
e) m 6 = _______
f) m 2 = _______
1
4
2
3
5
107°
6
Name ____________________________________
NR Geometry
Alternate Interior Angles
Proving Parallel Lines
Chp 4 Wksht #4
What We Know
When lines are parallel,
alternate interior angles are
______________
Alternate Exterior Angles
When lines are parallel,
alternate exterior angles are
______________
Corresponding Angles
When lines are parallel,
corresponding angles are
______________
Co-Interior Angles
When lines are parallel,
co-interior angles are
______________
When you don’t know whether or not a pair of lines is parallel, you can use the opposite of these statements to
prove whether or not they are.
Alternate Interior Angles
Proving Lines Parallel
If alternate interior angles
are ______________, then
lines are parallel.
Alternate Exterior Angles
If alternate exterior angles
are ______________, then
lines are parallel.
Corresponding Angles
If corresponding angles are
______________, then
lines are parallel.
Co-Interior Angles
If co-interior angles are
______________, then
lines are parallel.
1. Which figure contains a pair of parallel lines? (Multiple Choice)
Proofs: Fill in the blanks with the options from the box in each problem
6.) Given: BD bisects ABC ,
1  2
A
D 1
2 3
B
Prove: AD BC
C
Statements
1.
Reasons
1.Given
2.
2.Given
3.
3.Definition of Angle Bisector
4.
4.If two things are equal to the same thing, then they are
equal (transitive property)
5.
5. AD BC
1  3 / 1  2 /
If corresponding angles are congruent
then lines are parallel/ 2  3 / BD bisects ABC
Name ____________________________________
NR Geometry
Chapter Review
Chp 4 Wksht #5
Vocabulary:
Alternate Exterior
Alternate Interior
Corresponding
Co-Interior
Transversal
Examples:
1. In the diagram, parallel lines m and n are cut by transversal t.
I.) Name the following angle pairs and their relationship (  or supplementary):
a. 1 and 8 __________________________________
b. 2 and 6 __________________________________
c. 3 and 5 __________________________________
d. 2 and 7 __________________________________
e. 4 and 5 __________________________________
f. 6 and 7 __________________________________
e. 7 and 8 __________________________________
II.) Given the information, solve for the given angle:
a. If m4  42 , then m8  ________
b. If m6  156 , then m4  ________
c. If m1  3x  12 , and m5  6 x  42 , then m5  ________
d. If m2  4x  10 , and m8  3x  2 , then m2  ________ and m8  ________
2. In the diagram, lines r, s, and p are parallel to each other.
a. Name at least two angles congruent to 6
b. Name an angle congruent to 3
c. If m4  43 , and m9  39 , then m7  ______