SOL G.2

Name: _______________________________________________ Date: ____________________

Chapter 3

Parallel and

Perpendicular LinesSections Covered:

3.1 Identify Pairs of Lines and Angles 3.2 Use Parallel Lines and Transversals

3.3 Prove Lines are Parallel 3.4 Find and Use Slopes of Lines

3.5 Write and Graph Equations of Lines

The student will use the relationships between angles formed by two lines cut by a transversal to

a) determine whether two lines are parallel;b) verify the parallelism, using algebraic and coordinate methods as

well as deductive proofs; andc) solve real-world problems involving angles formed when parallel lines

are cut by a transversal.

The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include

a) investigating and using formulas for finding distance, midpoint, and slope;

b) applying slope to verify and determine whether lines are parallel or perpendicular;

SOL G.3

Unit 3 Syllabus: Ch 3 Parallel and Perpendicular Lines Block

Date Topic Homework

16 B 10/16A 10/17

3.1 Identifying Lines and Angles3.2 Angle Relationships and Parallel Lines

Worksheet: 3.1 and 3.2 Identifying Lines and Angle Relationships

17 B 10/20A 10/21

3.3 Proving Lines Parallel Worksheet: 3.3 Proving Lines Parallel

18 B 10/22A 10/23

Quiz 3.1-3.3 Khan Academy

19 B 10/24A 10/27

3.4 Slope of Lines3.5 Writing Equations of Lines

Worksheet: 3.4 Slope of Lines3.5 Writing Equations of Lines

20 B 10/28A 10/29

Review Ch 1 and 2 for Quarter Test

Review Worksheet—Separate from packet

21 B 10/30A 10/31

Quarter 1 Benchmark Test Review Worksheet #1

1 B 11/5A 11/6

Review Day Ch 3 Review Worksheet #2

2 B 11/7A 11/8

Ch 3 Test Khan Academy

***Syllabus subject to change due to weather, pep rallies, illness, etc

Need Help?Email your teacher to set up a time before or after school!Peer Tutoring is available through Mu Alpha Theta is Monday, Tuesday, Thursday, and Friday mornings in L403.

Need to make up a test/quiz?Math Make Up Room is open Tuesday, Thursday, and Friday mornings and Monday, Wednesday, and Thursday afternoons.

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Notes 3.1 & 3.2: Identifying Lines and Angles and Angle Relationships

_______________________________________________________

PARALLEL PERPENDICULAR SKEW

DEFINITION

LINES- LINES- LINES-

EXAMPLE

DEFINITION

PLANES- PLANES-

EXAMPLE

Think of each segment in the diagram as part of a line. Which line(s) or plane(s) appear to fit the description?

1. Line(s) parallel to AB

2. Line(s) perpendicular to BF

3

B

E

DA

H

G

C

F

B

E

DA

H

G

C

F

J

N

L

M

P

K

B

E

DA

H

G

C

F

J

N

L

M

P

K

3. Line(s) skew to CD and containing point E

4. Plane(s) perpendicular to plane ABE

5. Plane(s) parallel to plane ABC

4

This table defines the five types of angles by their location. It also states the specific relationships they have when the transversal cuts through parallel lines.

Type: Location: Picture:

Theorem: If 2 parallel lines are cut by a transversal, then ___________________________ are _______________.

Type: Location: Picture:

Theorem: If 2 parallel lines are cut by a transversal, then ___________________________ are _______________.Type: Location: Picture:

Theorem: If 2 parallel lines are cut by a transversal, then ___________________________ are _______________.

Type: Location: Picture:

Theorem: If 2 parallel lines are cut by a transversal, then ___________________________ are _______________.

Type: Location: Picture:

Theorem: If 2 parallel lines are cut by a transversal, then ___________________________ are _______________.

Classify each angle pair as corresponding, alternate interior, alternate exterior, consecutive interior, or consecutive exterior.

a) ∠1 and ∠9 ____________________5

b) ∠8 and ∠13 ____________________

c) ∠6 and ∠16 ____________________

d) ∠4 and ∠10 ____________________

e) ∠8 and ∠16 ____________________

f) ∠10 and ∠13 ____________________

Discovery: Lines l and m are parallel. Note: Parallel lines are distinguished by a matching set of arrows on the lines that are parallel. Find the measure of the missing angles by using transparent paper. Then, let’s go back and fill in the theorems.

Key Question: If x = 115°, is it possible for y to equal 115°?

For t he following diagrams, state the type of angles that are given, state their relationship, and then find x.

1. 2. 3.

6

115°

x° y°

z°

l

m

Find the missing variables.

4. 5. 6.

On Your Own: For t he following diagrams, state the type of angles that are given, state their relationship, and then find x.

1. 2. 3.

4. 5. 6.

7

60°(3x + 15)°

(–5y – 10)°

75°

(5x – 10)°(10y – 25)°

100°

(x – 10)°(2y + 24)°

120°

3x°

(6y – 12)°

Notes 3.3: Proving Lines Parallel

_______________________________________________________Follow along and fill in the missing blanks for each theorem. Then, based on the theorem, use the given theorem to determine if the lines are parallel or not parallel. Provide reasoning.

Corresponding Angles Converse Theorem: If 2 lines are cut by a transversal so the corresponding angles are __________________, then the lines are __________________. Example: Non Example:

Alternate Interior Angles Converse Theorem: If 2 lines are cut by a transversal so the alternate interior angles are __________________, then the lines are __________________.Example: Non Example:

Alternate Exterior Angles Converse Theorem: If 2 lines are cut by a transversal so the alternate exterior angles are __________________, then the lines are __________________.Example: Non Example:

Consecutive Interior Angles Converse Theorem: If 2 lines are cut by a transversal so the consecutive interior angles are __________________, then the lines are __________________.

8

92°l

k88°

j

k

3

6

l

k

2

6

j

k

25°j

k105°

130°

28° l

k

106°

137°

Example: Non Example:

9

96°j

k84°

HK

J I

Consecutive Exterior Angles Converse Theorem: If 2 lines are cut by a transversal so the consecutive exterior angles are __________________, then the lines are __________________.

Transitive Property of Parallel Lines:

Example:

Is it possible to prove the lines are parallel or not parallel? If so, state the postulate or theorem you would use. If not, state cannot be determined.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10

u tp

92° l

k88°

l

k

122°

l

k

58° m

105° 75°A B

CD

55°

55°

E

F

GH

I

10. Find the value of x that makes l // m.

11. a. Find the value of x that makes a // b. b. Find the value of y that makes a // c.

c. Is b // c? Why or why not?

State the postulate or theorem that supports each conclusion.

1. Given: a || b ____________________ Conclusion: 2 7

2. Given: m 4 + m 7 = 180 ____________________ Conclusion: a || b

3. Given: 4 5 ____________________ Conclusion: a || b

11

a b

1 2 3 4

5 6 7 8

Find the values of x and y. Explain your reasoning by stating the proper theorem or postulate.

4. x = y =

_____________________ _____________________

5. x = y =

_____________________ _____________________

6. x = y =

_____________________ _____________________

Find the value of x so that n || m. State the theorem or postulate that justifies your solution.

7. 8. 9.

x = x = x =

_____________________ _____________________ _____________________

Can you prove that lines p and q are parallel? If so, state the theorem or postulate that you would use.

10. 11. 12.

_____________________ _____________________ _____________________

12

x y

130

x y 65

x y

80

n n n m

m m5x

3x+45x+2 7x+1

5x-18

8x-5

pq

qp

q

p

Notes 3.4 and 3.5: Writing Equations of Lines

_______________________________________________________

Equations of Lines and Slope Slope intercept form: Slope Formula:

Graphing and Types of Slopes: Graph the following lines.

y = 2x + 4 y = x – 2 y = – 3 x = 5

m = ______ b = ______

m = _____ b = ______

Acronym: Acronym:

type of slope: type of slope: type of slope: type of slope:

For each equation, rewrite in slope-intercept form and state the m & b values.

3y – 8x = 2

m=_________b=_________

9x = 4y – 11

m=_________b=_________ m=_________b=_________

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Special Types of Lines:

TYPE OF LINE PARALLEL LINES PERPENDICULAR LINES

DEFINITION

SLOPES OF THESE TYPE OF LINES

State the negative reciprocal of the given slope.1. m = 2. m = –6 3. m = 4. m = 9

Find the slope of the given lines. j passes through (0, 3) and (3, 1)

m passes through ( –2, 7) and (–6 , 1)

k passes through (-4, -3) & (0, 3)

Make some conclusions. Make a quick sketch to see what parallel and perpendicular lines look like.

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15

Write the equation of a line in slope intercept form:Steps: 1. Ask yourself “What two letters do I need to write the equation of a line?”

2. Identify which letters you need to still find.3. If you need m, plug the points into the slope formula.4. If you need b, plug m and an ordered pair (x, y) into the slope intercept

formula and solve for b.5. Write the equation of a line with the new m and b.

TYPE I: Write the equation of the line that passes through the given y-intercept and given slope.1. m = 3, b = -3 2. m = , b = 15

TYPE II: Write the equation of the line that passes through the given point and given slope.

3. Passes through (2, 3) and slope is 5.

4. Passes through (6, -5) and slope is

5. Passes through (5, -2) and slope is 0. Remember: You can always check the b

by graphing. Plot the point and move by counting the slope till you cross the y-

axis.

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Type III: Write the equation of a line given two points.

6. Passes through (4, -3) and (3, -6) 7.

TYPE IV: Write the equation of a line given two points and must be parallel or perpendicular to another line. 8. Passes through (3, 2) 9. Passes through (4, 0) Parallel to Perpendicular to 2x + y = 1

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Practice: Are these equations parallel, perpendicular, or neither?1. l: h: 2. q: w:

3. Which lines are //? Which are ⊥? A graph may help.

x = 4y = –4 y = 4x

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