Chapter 3: Basic Angle Relationships
CHAPTER 3: BASIC ANGLE RELATIONSHIPS
# Name
1 Video: Understanding Angles
2 Angle Pair Relationships
3 Lab: Discovering Angles from Parallel Lines
4 Identifying Lines, Angles and Relationships
5 Angles within Parallel Lines
6 Proving Parallel Lines
7 Chapter Review
8 Chapter TEST
Name ___________________________________
Complete?
Score ____/10
October/November
26
Chapter 2 Test
27
#4 Identifying
Lines, Angles and
Relationships
2
#5 Angles within
Parallel Lines
3
Early Release 28
Geometry
Documents on the
Calculator
HW: Video #1
#2 Angle Pair
Relationships
4
#6 Proving Parallel
Lines
5
#7 Chapter Review
29 30
#3 Lab:
Discovering Angles from Parallel Lines
6
Chapter TEST
No Skills Quiz
Name __________________________________
CC Geometry
Vocabulary
Complementary:
Supplementary:
Adjacent:
Linear:
Vertical:
Video: Understanding Angles
Chp 3 Wksht #1
Angle 1 and Angle 2 are supplementary. If angle 1 = 2x+7 and angle 2 = 4x-7, what is the measure of angle 1?
1.
2.
3.
4.
5.
6.
Name the following and solve for the missing angles.
Angle 1 = 125 o
Angle 4 =
Angle 2 = Angle 3 = 91 o
Angle 5 = Angle 6 =
Name __________________________________
CC Geometry
Angle Pair Relationships
Chp 3 Wksht #2
Name the relationship: complementary, supplementary, vertical or adjacent. Find a or b.
Find the measure of the missing angle(s).
Find the value of x SHOW WORK!
Name ____________________________________
CC Geometry
Lab: Discovering Angles from Parallel Lines
Chp 3 Wksht #3
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
3. m
CAB
5. m
ABJ
7. m
EBG
2.
4.
6.
8. m m m m
DAC
FAB
ABE
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 m e asures.
1. m
DAF
3. m
CAB
5. m
ABJ
2. m
DAC
4.
6. m m
FAB
ABE
7. m
EBG
8. What do you notice about the measurements?
9.
Also called co-interior angles
8. m
JBG
Name the relationship for each pair of angles. a.)
DAF and
ABJ b.)
DAF and
EBG c.)
DAC and
JBG e.)
CAB and
ABJ g.)
CAB and
EBA d.) f.) h.)
DAC
EBA
FAB
and
ABE and
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.) x+10
3x b.) x x+10 c.) Find the measure of angle 3 x
3
4x d.) Find the measure of all the missing angles
77 o 45 o
Name ____________________________________
CC Geometry
Identifying Lines, Angles and Relationships
Chp 3 Wksht #4
1. Solve the following. a) x = ________ y = ________ b) x = ________ y = ________ c) x = ________ y = ________
67° x y
3x - 5 y
127°
5x - 15 y
2. 5 and 3 are vertical angles.
3.
1 and
5 are a linear pair.
4.
4 and
3 are adjacent angles.
5.
4 and
1 are vertical angles.
6.
3 and
4 are a linear pair.
T or F
T or F
T or F
T or F
T or F
1
2
5
3
4
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 _______________ e)
1 &
7 ________________ f)
6 &
5 ________________ g)
15 &
10 ________________ h)
1 &
2 ________________ i)
13 &
12 ________________ j)
16 &
9 ________________
1
3
2
4
6
7
5
8
16
13
15
14
12
9
11
10
13. Find the measure of the angle and give a reason for knowing it.
(measure) (reason) a) m
1 = ___________ _______________________ b) m
2 = ___________ _______________________ c) m
3 = ___________ _______________________ d) m
4 = ___________ _______________________ e) m
5 = ___________ _______________________
110°
1
5
4
2
3
50°
14. Find the measure of the angle. a) m
1 = ___________ b) m
2 = ___________ c) m
3 = ___________ d) m
4 = ___________ e) m
5 = ___________ f) m
6 = ___________
15. Circle (T)rue or (F)alse. a)
1
4 T or F c)
3
5 T or F e)
2
10 T or F b) d)
6
4
16
5
T or F
T or F f)
9
15 T or F g)
12
14 T or F h)
9
11 T or F i) m
11 + m
15 = 180
T or F j) m
1 + m
8 = 180
T or F
16. Solve for the unknown values. a) x = ___________ b) x = ___________
8x - 4
3x + 16
5x - 10
160° d) x = ___________ e) x = ___________
2
1
83°
6
3
5
4
1
3
2
4
5 6
8 7 c) x = ___________
2x + 13 f) x = ___________
9 10
12 11
13 14
16 15
3x + 17
118°
109°
4x + 32
5x - 7
3x + 16
172°
Name ____________________________________
CC Geometry
Angles within Parallel Lines
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 = _______ i) if m
1 + m
5 = 234
, find m
6 = _______
Chp 3 Wksht #5
4
1
3
2
8
5
7
6
2. Solve the following. a) m
1 = ____________ c) m
3 = ____________ e) m
5 = ____________ b) m
2 = ____________ d) m
4 = ____________ f) m
6 = ____________
32°
5
3
4
6
115°
1
2
3. Solve the following. a) x = ________ y = ________
4x - 5
3y + 1 b) x = ________ y = ________
9x + 12
6y
13y - 10
3x + 11
4. Solve a) m
6 = _______ b) m
7 = _______ c) m
4 = _______ d) m
2 = _______ e) m
5 = _______ f) m
8 = _______
6. Solve a) m
5 = _______ b) m
1 = _______ c) m
4 = _______ d) m
6 = _______ e) m
2 = _______
D
A
3
4
2
131°
42°
54°
B
6
C
4
8
7
5
6
18°
5
1
2
5. Solve a) m
7 = _______ b) m
5 = _______ c) m
6 = _______ d) m
4 = _______ e) m
8 = _______
7. Solve a) m
3 = _______ b) m
5 = _______ c) m
1 = _______ d) m
4 = _______ e) m
6 = _______ f) m
2 = _______
2
1
58°
6
7
5
8
4
47°
26°
48°
3
5
107°
4
6
Name ____________________________________
CC Geometry
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Co-Interior Angles
Proving Parallel Lines
Chp 3 Wksht #6
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Co-Interior Angles
What We Know
When lines are parallel, alternate interior angles are
______________
When lines are parallel, alternate exterior angles are
______________
When lines are parallel, corresponding angles are
______________
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.
Proving Lines Parallel
If alternate interior angles are ______________, then lines are parallel.
If alternate exterior angles are ______________, then lines are parallel.
If corresponding angles are
______________, then lines are parallel.
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
1
2
ABC ,
A
Prove: AD BC
2 3
B
D 1
Statements
1.
2.
3.
4.
5. AD BC
Reasons
1.Given
2.Given
3.Definition of Angle Bisector
C
4.If two things are equal to the same thing, then they are equal (transitive property)
5.
1
3
/
1
2
/ If corresponding angles are congruent then lines are parallel/
2
3
/
BD
bisects
ABC
Name ____________________________________
CC Geometry
Vocabulary:
Alternate Exterior Alternate Interior Corresponding
Chapter Review
Chp 3 Wksht #7
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
3 x
12 , and m
5
6 x
42 , then m
5
________ d. If m
2
4 x
10 , and m
8
3 x
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
______
