8-2

8-2 Classifying Angles

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm Up

Course 2

8-2 Classifying Angles

1. What percent of the model is shaded?

2. Find the value of 52 + 53.

3. What is the percent of change if 20 is increased to 25?

4. On a scale drawing of a tree with a scale of 1 cm = 0.9 m, the height of the tree is 1.2 cm. What is the actual height of the tree?

71%

150

25%

1.08 m

An angle is formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex.

Angles are measured in degrees (°).

A

CB

1

Vertex

Course 2

8-2 Classifying Angles

Learn to identify angles and angle pairs.

An angle’s measure determines the type of angle it is.

A right angle is an angle that that measures exactly 90°. Thesymbol indicates a right angle.An acute angle is an anglethat measures less than 90°.

An obtuse angle is an anglethat measures more than 90°but less than180°.

A straight angle is an anglethat measures 180°.

Course 2

8-2 Classifying Angles

Tell whether each angle is acute, right, obtuse or straight.

A. B.

obtuse angle acute angle

Course 2

8-2 Classifying Angles

Insert Lesson Title Here

Tell whether each angle is acute, right, obtuse, or straight.

A. B.

straight angle acute angle

Course 2

8-2 Classifying Angles

If the sum of the measures of two angles is 90°,then the angles are complementary angles.

If the sum of the measures of two angles is 180°,then the angles are supplementary angles.

Course 2

8-2 Classifying Angles

Course 2

8-2 Classifying Angles

COmplementary

upplementary

C C= 90˚

= 180˚

+ 90˚

C

Course 2

8-2 Classifying Angles

You can name this angle ABC, CBA, B, or 1.

Reading Math

A •

B • • C

1

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Course 2

8-2 Classifying Angles

Since 60° + 30° = 90°, PMQ and OMP are complementary.

O

P Q

M

OMP and PMQ

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Course 2

8-2 Classifying Angles

O

N R

M

Since 15° + 165° = 180°, NMO and OMR are supplementary.

Read mNMO as “the measure of angle NMO.”

Reading Math

NMO and OMR

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Course 2

8-2 Classifying Angles

PMQ and QMR P Q

RM

Since 30° + 75° = 105°, PMQ and QMR are neither complementary or supplementary.

Angles A and B are complementary.

If mA is 56°, what is the mB?

Course 2

8-2 Classifying Angles

Angles P and Q are supplementary.

If mP is 32°, what is the mQ?

One way to classify triangles is by the lengths of their sides.

Course 2

8-6 Classifying Triangles

Learn to classify triangles by their side lengths and angle measures.

Triangles classified by sides

A scalene trianglehas no congruent sides.

Course 2

8-6 Classifying Triangles

Triangles classified by sides

An isosceles trianglehas 2 congruent sides

Course 2

8-6 Classifying Triangles

Triangles classified by sides

In an equilateral triangle, all of the sides are congruent.

Course 2

8-6 Classifying Triangles

Another way to classify triangles is by the measures of their angles.

Triangles classified by angles

In an acute triangle, all of the angles are acute.

Course 2

8-6 Classifying Triangles

Triangles classified by angles

An obtuse triangle hasone obtuse angle.

Course 2

8-6 Classifying Triangles

Triangles classified by angles

A right triangle has one right angle.

Course 2

8-6 Classifying Triangles

Classify each triangle according to its sides and angles.

A. Two congruent sidesacute Three acute angles

This is an isosceles acute triangle.

B. No congruent sidesright One right angle

This is a scalene right triangle.

isosceles

scalene

Course 2

8-6 Classifying Triangles

Classify each triangle according to its sides and angles.

C. Three congruent sides

acute Three acute angles

This is an equilateral acute triangle.

equilateral

Course 2

8-6 Classifying Triangles

D. No congruent sides

obtuse One obtuse angle (exceeds 90°)

This is a scalene obtuse triangle.

scalene

Insert Lesson Title Here

Classify each triangle according to its sides and angles.

E. Two congruent sidesobtuse One obtuse angle

This is an isosceles obtuse triangle.

F. Two congruent sides

right One right angle

This is an isosceles right triangle.

isosceles

isosceles

Course 2

8-6 Classifying Triangles

Identify the different types of triangles in the figure, and determine how many of each there are.

Type How many Name

Scalene 2 ABD, BCD

Isosceles

Right

Obtuse

Acute

ACE, ABC

ABD, BCD

ACE

ABC

2

2

1

1

Course 2

8-6 Classifying Triangles

Insert Lesson Title Here

A

BC

D

EF

G

H

I J

Identify the different types of triangles in the figure, and determine how many of each there are.

Isosceles

Obtuse

Acute

5

2

4

NameHow manyType

DJA, JDG

HJI, BCD

DFE

DJA, ADG

JDG, JHI,

BCD, DEF

Course 2

8-6 Classifying Triangles

Lesson Quiz

Classify each triangle according to its sides and angles.

1. 7ft, 8ft, 12ft

2. 45°, 90°, 45°

3. 12, 9, 12

4. 120°, 20°, 40°

5. Identify the different types of triangles in the figure and determine how many of each there are.

right

scalene

Insert Lesson Title Here

isosceles

obtuse

1 isosceles acute triangle, 1 equilateral triangle, 1 scalene right triangle

Course 2

8-6 Classifying Triangles