Classifying Triangles

What do we remember about classifying angles?

What are the different types of angles?

Acute, right, obtuse, and straight

How are triangles classified?

Triangles are classified in two ways: by their sides and their angles

Types of triangles classified by their sides

EquilateralIsoscelesScalene

Types of triangles classified by their angles

AcuteRightObtuse

Equilateral Triangles

All 3 sides are congruent

(Note: all 3 angles are congruent also)

Equilateral Triangles cont’d

Isosceles Triangles

2 sides are congruent

(Note: base angles are also congruent)

Isosceles Triangle cont’d

Scalene Triangle No sides are congruent

Scalene Triangle

Acute Triangle All 3 angles are acute

Acute Triangle

Right Triangle Has 1 right angle

Right Triangle

Obtuse Triangle Has 1 obtuse angle

Obtuse Triangle

Multiple Classifications

Triangles can be classified by both their sides and angles:

Acute IsoscelesRight IsoscelesObtuse IsoscelesAcute ScaleneObtuse ScaleneRight Scalene

What type of triangle does not have multiple classifications?

Equilateral Triangles – all of its angles and sides are congruent, so there cannot be different types of equilateral triangles.

Acute Isosceles Triangle

2 sides are congruent and all angles are acute

Obtuse Isosceles Triangle

2 sides are congruent and one angle is obtuse

Right Isosceles Triangle

2 sides are congruent and one angle is a right angle

Acute Scalene Triangle

No sides are congruent and all angles are acute

Obtuse Scalene Triangle

No sides are congruent and one angle is obtuse

Right Scalene Triangle

No sides are congruent and one angle is a right angle

Two sets of questions we should ask ourselves when classifying triangles:

1. Regarding angles:Are all 3 angles acute, or is 1 angle right or obtuse?

2. Regarding sides:Are all 3 sides congruent, are only 2 sides congruent, or are no sides congruent?

For you to try: what type of triangles are the following triangles?