8.1 angles 2

Lesson 8.1, For use with pages 403-408

Solve the equation.

1. 7w = 56 2. = 21v3

Lesson 8.1, For use with pages 403-408

Solve the equation.

1. 7w = 56

ANSWER 8 ANSWER 63

2. = 21v3

Chapter 8.1

Lines and Angles

Chapter 8 Section 1

• Vocabulary 15-22

Essential Questions

• Why is it important to be able to identify congruent triangles in everyday life?

• Where in real life can you use the properties of isosceles and equilateral triangles?

• How are the relationships between lines and planes used in the real world?

• What areas in the real world are properties of parallel lines important?

12

34

56

78

t

4 and 2 3 and 15 and 76 and 8

Corresponding angles: any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

Corresponding Angles

• Name the angle relationship

• Are they congruent or supplementary?

• Find the value of x

x

t

151

Interior Angles

• any of the four angles formed in the area between a pair of parallel lines when a third line cuts them

t

C

A B

D

Interior Angles

• Name the angle relationship

• Are they congruent or supplementary?

• Find the value of x

81

t

x

supp

Exterior Angles

• an angle formed by a transversal as it cuts one of two lines and situated on the outside of the line

t

C

A B

D

Alternate Interior Angles

3 and 72 and 6

12

34

56

78

t

When two lines are crossed by another line, the pairs of angles on opposite sides of the transversal but inside the two lines.

Alternate Interior Angles

• Name the angle relationship

• Are they congruent or supplementary?

• Find the value of x

126

t

x

Alternate Exterior Angles

5 and 14 and 8

12

34

56

78

t

When two lines are crossed by another line, the pairs of angles on opposite sides of the transversal but outside the two lines.

Alternate Exterior Angles

• Name the angle relationship

• Are they congruent or supplementary?

• Find the value of x

125

t

x

List all pairs of angles that fit the description.

a. Corresponding

b. Alternate Interior

c. Alternate Exterior1

23

45

67

8t

Find all angle measures

1 67

3

t

113

180 - 67

2

5

6 7

8

67

67

67

113

113

113

Congruent Angles

• Angles that have the same measure

Perpendicular Lines

• Lines that intersect and form 90 ° angles are called perpendicular lines.

Perpendicular Lines

• These 4 angles are also form VERTICAL and SUPPLEMENTARY angles.

Parallel Lines• Two lines in the same plane that do not

intersect.

SOLUTION

EXAMPLE 3 Using Parallel Lines

Use the diagram to find the angle measure.

a. m 1b. m 2

a. 1 and 5 are corresponding angles, so they have equal measures. You can find m 5 because it is the supplement of the given angle.

m 5 = 55Definition of supplementary angles

Subtract 125 from each side.

ANSWER m 1= 55

m 5 + 125 = 180

55° 125°

125° 55°

55° 126°

55°

GUIDED PRACTICE for Example 3

SOLUTION

m 2 and the given angle are corresponding angles, so they have equal measures.

ANSWER m 2 = 85

9. m 2

Find the angle measure.

85°

95°

95°

85° 95°85°

95°

• Assignment: P. 406 #12-23, 28-31