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?