Classify triangles by angles and sides Classify triangles using the Pythagorean Theorem

1. Classifying Triangles
The student is able to (I can):
• Classify triangles by angles and by sides
• Classify triangles using the Pythagorean Theorem

2. Classifying Triangles
Triangles are classified by their side lengths and their angle
measures as follows:
• By side length
– equilateral – all sides congruent (equal)
– isosceles – two or more sides congruent
– scalene – no sides congruent
• By angle measure
– acute – all acute angles
– right – one right angle
– obtuse – one obtuse angle
– equiangular – all angles congruent

3. Practice
Classify each triangle by its angles and sides.
1. 3.
2. 4.
90
110

4. Practice
Classify each triangle by its angles and sides.
1. 3.
2. 4.
90
110
right
scalene
equiangular
equilateral
acute
isosceles
obtuse
isosceles

5. Converse of the Pythagorean Theorem
If a2 + b2 = c2, then the triangle is a right triangle.
Another way to think of this is
Pythagorean Inequalities Theorem
If then the triangle is an obtuse triangle.
If then the triangle is an acute triangle.
2 2 2
,c a b +
2 2 2
,c a b +
2 2 2
.c a b= +

6. Classifying Triangles
right triangle
obtuse
triangle
acute
triangle
2 2 2
c a b + 2 2 2
c a b +2 2 2
c a b= +
a
b
c
a
b
c
a
b
c

7. Examples
Classify the following triangle measures as right, obtuse, or
acute.
1. 5, 7, 10
2. 30, 16, 34
3. 3.8, 4.1, 5.2

8. Examples
Classify the following triangle measures as right, obtuse, or
acute.
1. 5, 7, 10
102 = 100, 52 + 72 = 74 Obtuse
2. 30, 16, 34
342 = 1156, 162 + 302 = 1156 Right
3. 3.8, 4.1, 5.2
5.22 = 27.04, 3.82 + 4.12 = 31.25 Acute