6.2 Classifying Triangles

Classify triangles by angles and by sides
Analyze the relationship between the angles and sides of a triangle
Determine allowable lengths for sides of triangles

1. Classifying Triangles
The student is able to (I can):
• Classify triangles by angles and by sides
• Analyze the relationship between the angles of a t riangle
and the lengths of the sides
• Determine allowable lengths for sides of triangles

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 or more or more or moresides 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. If two sides of a triangle are not congruent, then the larger
angle is opposite the longer side.
If two angles of a triangle are not congruent, then the longer
side is opposite the larger angle.
A
C
T
AT> AC→m∠C> m∠T
m∠C> m∠T→AT> AC

6. Example: Given the side lengths, put the angles in order
from smallest to largest.
∠Pis across from 16, ∠Nis across from 19, and ∠Ais
across from 31, so it would be: ∠P, ∠N, and ∠A
P
A
N
19
31
16

7. Example: Given the angle measures, put the side le ngths in
order from smallest to largest.
First, we have to calculate m ∠E:
m∠E= 180-(70+30) = 80°
So the sides would be:
TE< EN< TN
T
E
N
70°30°

8. Triangle Inequality Theorem The sum of any two side lengths of a triangle is gr eater than
the third side length.
Example:
1. Which set of lengths forms a triangle?
4, 5, 10 7, 9, 12
4 + 5 < 10 T7 + 9 > 12 h

9. Note: To find a range of possible third sides give n two sides,
subtract for the lower bound and add for the upper
bound.
Examples:
2. What is a possible third side for a triangle wit h sides 8 and
14?
14 –8 = 6 lower bound
14 + 8 = 22 upper bound
The third side can be between 6 and 22.

10. 3. What is the range of values for the third side of a triangle
with sides 11 and 19?
19 –11 = 8 lower bound
19 + 11 = 30 upper bound
8 < x< 30