Daily Homework Quiz For use after Lesson 7.3

Use a percent proportion to answer the question.

1. 28 is what percent of 80? 2. 15 is 5% of what number?

Daily Homework Quiz For use after Lesson 7.3

Use a percent proportion to answer the question.

ANSWER 35%

1. 28 is what percent of 80? 2. 15 is 5% of what number?

ANSWER 300

Chapter 8.1

Lines and Angles

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?

Chapter 8 Section 1

• Vocabulary 1-14

Prerequisite Skills VOCABULARY CHECK

APoint: a figure without dimensions.

Line: a figure that extends without end in two opposite directions.

X Y XY

Ray: a figure that has one endpoint and extends without end in one direction.

C D CD

• Plane : A flat surface that extends without end.

• Angle: a figure formed by two rays that begin at a common point called the vertex.

C

A

B

Vertex

Vertex: end point of the rays that form an angle.

• Degree: unit of measure. 950

Prerequisite Skills VOCABULARY CHECK

Identify the object with the review word from the list: point, line, ray, plane, angle, vertex, degree.

2.

1.

3.

ANSWER line

ANSWER point

ANSWER ray

4. A unit for measuring angles is a(n) ? .

ANSWER degree

Classifying Angles

• Angles are classified by degrees.

• Acute - greater than 0 degrees but less than 90 degrees.

C

A

BThis is read “Angle ABC or Angle CBA, or just Angle B

ABC

Classifying Angles

• Obtuse – angles measuring more than 90 degrees but less than 180 degrees.

Classifying Angles

• Right Angles measure exactly 90 degrees and labeled with “square” in the corner of the angle.

Classifying Angles• A straight angle “looks like” a straight line,

but it actually is an angle. It measures exactly 180 degrees.

A B C

180ABC m

Two angles are complementary if the sum of their measures is 90 degrees.

70 °

20 °

70 + 20 = 90 degrees.

• Are these complementary angles?

60 °

30 °

• Two angles are supplementary if the sum of their measures is 180 degrees.

1 2 180m m

1 2

GUIDED PRACTICE for Example 1

Tell whether 1 and 2 are complementary, supplementary, or neither.

1. m 1 = 79

m 2 = 101

SOLUTION

m 1+ m 2

= 79° + 101°

ANSWER

Hence, the angles are supplementary.

= 180

GUIDED PRACTICE for Example 1

Tell whether 1 and 2 are complementary, supplementary, or neither.

2. m 1 = 64

m 1 = 36

SOLUTION

m 1+ m 2

= 100°

= 64 + 36

ANSWER

Hence, 1 and 2 are neither complementary nor supplementary.

GUIDED PRACTICE for Example 1

Tell whether 1 and 2 are complementary, supplementary, or neither.

3. m 1 = 52

m 1 = 38

SOLUTION

m 1+ m 2

= 52 + 38

= 90

ANSWER

Hence, 1 and 2 are complementary.

Vertical AnglesWhen two lines intersect at a point, they form

two pairs of vertical angles. They do not share a side, and they have the same measure.

1

3 42

Angles 1 & 2 are vertical angles and 3&4 are vertical angles.

GUIDED PRACTICE for Example 2

Find the measures of the numbered angles.

SOLUTION

It is given that m 5 = 137 .

STEP 1

5 and 7 are vertical angles.Their measures are equal, so m 7 = 137 ° .

137°

43°

43°

GUIDED PRACTICE for Example 2

Find the measures of the numbered angles.

SOLUTION

It is given that m 8 = 54 .

STEP 1

8 and 10 are vertical angles. Their measures are equal, so m 10 = 54 ° .

54°

126°

126°

Homework

• Page 406 #1-11