Holt CA Course 1

9-6 Classifying Triangles

Preparation for MG2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle.)

California Standards

Holt CA Course 1

9-6 Classifying Triangles

Vocabulary

scalene triangleisosceles triangleequilateral triangleacute triangleobtuse triangleright triangle

Holt CA Course 1

9-6 Classifying TrianglesOne way to classify triangles is by the lengths of their sides.

Triangles classified by sides

A scalene trianglehas no congruent sides.

Holt CA Course 1

9-6 Classifying TrianglesOne way to classify triangles is by the lengths of their sides.

Triangles classified by sides

An isosceles trianglehas at least 2 congruent sides.

Holt CA Course 1

9-6 Classifying TrianglesOne 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.

Holt CA Course 1

9-6 Classifying TrianglesOne 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.

Holt CA Course 1

9-6 Classifying TrianglesOne 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.

Holt CA Course 1

9-6 Classifying TrianglesOne 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 exactly one right angle.

Holt CA Course 1

9-6 Classifying Triangles

Classify each triangle according to its sides and angles.

Additional Example 1: Classifying Triangles

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

Holt CA Course 1

9-6 Classifying Triangles

Classify each triangle according to its sides and angles.

Additional Example 1: Classifying Triangles

C. Three congruent sides

acute Three acute angles

This is an equilateral acute triangle.

D. No congruent sides

right One right angle

This is a scalene right triangle.

equilateral

scalene

Holt CA Course 1

9-6 Classifying Triangles

Check It Out! Example 1

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.

isosceles

isosceles

Holt CA Course 1

9-6 Classifying Triangles

Check It Out! Example 1

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

Holt CA Course 1

9-6 Classifying Triangles

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

Additional Example 2: Identifying Triangles

Type How many Name

Scalene 2 ABD, CBD

Isosceles

Right

Obtuse

Acute

ACE, ABC

ABD, CBD

ACE

ABC

2

2

1

1

Holt CA Course 1

9-6 Classifying TrianglesCheck It Out! Example 2

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