7-6

7-6 Triangles

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm Up1. What is the name of a six-sided figure?

2. What is the definition of an acute angle?

3. The measure of one angle of two supplementary angles is 32°. What is the measure of the other angle?

hexagon

an angle that measures less than 90°

148°

Course 2

7-6 Triangles

Problem of the Day

Use 6 congruent line segments to form 4 equilateral triangles. (Hint: Use toothpicks or other objects to model the segments.) Place the segments so they form a pyramid.

Course 2

7-6 Triangles

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

Course 2

7-6 Triangles

Vocabulary

scalene triangleisosceles triangleequilateral triangleacute triangleobtuse triangleright triangle

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Course 2

7-6 Triangles

Course 2

7-6 Triangles

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

Triangles classified by sides

A scalene trianglehas no congruent sides.

Course 2

7-6 Triangles

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

Triangles classified by sides

An isosceles trianglehas at least 2 congruent sides

Course 2

7-6 Triangles

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

Triangles classified by sides

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

Course 2

7-6 Triangles

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

Triangles classified by angles

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

Course 2

7-6 Triangles

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

Triangles classified by angles

An obtuse triangle hasone obtuse angle.

Course 2

7-6 Triangles

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

Triangles classified by angles

A right triangle has one right angle.

Course 2

7-6 Triangles

When classifying a triangle according to its sides and angles, use the word that describes the sides first, and use the word that describes its angles second.

Writing Math

Classify each triangle according to its sides and angles.

Additional Example 1A & 1B: Classifying Triangles

Course 2

7-6 Triangles

A. Two congruent sidesacute Three acute angles

This is an isosceles acute triangle.

5 ft

9 ft9 ft

B. No congruent sidesright One right angle

This is a scalene right triangle.

24 m 25 m

7 m

isosceles

scalene

Classify each triangle according to its sides and angles.

Additional Example 1C & 1D: Classifying Triangles

Course 2

7-6 Triangles

C. No congruent sides

acute Three acute angles

This is a scalene acute triangle.

D. Three congruent sides

acute Three acute angles

This is an equilateral acute triangle.

scalene

equilateral

Try This: Example 1A & 1B

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Course 2

7-6 Triangles

Classify each triangle according to its sides and angles.

A. Two congruent sidesobtuse One obtuse angle

This is an isosceles obtuse triangle.

B. Two congruent sides

right One right angle

This is an isosceles right triangle.

5 ft

3 ft 3 ftisosceles

isosceles

Try This: Example 1C & 1D

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Course 2

7-6 Triangles

Classify each triangle according to its sides and angles.

C. No congruent sidesobtuse One angle exceeding 90°

This is a scalene obtuse triangle.

D. No congruent sides

obtuse One angle exceeding 90°

This is a scalene obtuse triangle.

scalene

scalene

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

Additional Example 2: Identifying Triangles

Course 2

7-6 Triangles

Type How many Name

Scalene 2 ABD, BCD

Isosceles

Right

Obtuse

Acute

ACE, ABC

ABD, BCD

ACE

ABC

2

2

1

1

Try This: Example 2

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Course 2

7-6 Triangles

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

Lesson Quiz

Classify each triangle according to its side or angle measures.

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

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isosceles

obtuse

Course 2

7-6 Triangles

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