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5.1
Classifying Triangles
SWBAT classify triangles in
the coordinate plane
Classification means
put things into a
group according to
how they are alike.
We will break this group of
animals into smaller groups.
The same animals can be put into
different groups depending on what
we look at when we classify them.
Today you will learn how
triangles can be classified
in two different ways...
Think of all the different kinds
of triangles you know.
Did you come up with all of these?
Acute
Obtuse
Right
Scalene
Isosceles
Equilateral
Triangle

A polygon with 3 sides.
 The
three endpoints are called vertices.
Classifying by side lengths
Scalene
Isosceles
Equilateral
Scalene Triangle
 All
sides are different lengths.
Isosceles Triangle
 At
least two out of the three sides
are equal lengths.
Equilateral Triangle
 All
sides have the same length
Classify this triangle by its sides.
Classify this triangle by its sides.
Classify this triangle by its sides.
Classify the following triangles by
their sides. Use these signals:
Scalene
Isosceles
Equilateral
Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral
Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral
Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral

What formula do you use to determine if a
triangle is scalene, isosceles, or
equilateral?
Answer: The terms scalene, isosceles, and
equilateral have to do with side lengths of a
triangle so you use the Distance Formula.
Classifying by angle measures
Right
Acute
Obtuse
Acute Triangle
All three angles are less than 900.
800
400 600
Obtuse Triangle
One of the three angles is more than 900
200
1300
300
Right Triangle
One of the three angles is exactly 900
Classify the following triangles by
their sides. Use these signals:
Acute
Obtuse
Right
Classify by angles.
Acute
Obtuse
Right
Classify by angles.
1000
Acute
Obtuse
Right
Classify by angles.
850
450
500
Acute
Obtuse
Right
B
A
D
C
E
Now you should be able to classify
any triangle by both its side
lengths and its angles.
Classify the triangles by sides lengths
and angles
a)
b)
7
c)
40°
15°
25
24
70°
70°
120°
Solutions:
a) Scalene, Right
b) Isosceles, Acute
c) Scalene, Obtuse
45°
Example 1
Classify a triangle in a coordinate plane
Determine whether PQO with vertices
at P(-1, 2), Q(6, 3), O(0, 0), is scalene,
isosceles, or equilateral. Explain.
SOLUTION Use the distance formula to find the side lengths.
OP =
=
( x2 – x1 ) 2 + ( y2 – y1 ) 2
( (– 1 ) – 0 ) 2 + ( 2 – 0 ) 2 =
5
2.2
=
45
6.7
( 6 – (– 1 )) 2 + ( 3 – 2 ) 2 =
50
7.1
OQ =
( x2 – x1 ) 2 + ( y2 – y1 ) 2
=
PQ =
( 6 – 0 )2 + ( 3 – 0 )2
( x2 – x1 ) 2 + ( y2 – y1 ) 2
=
EXAMPLE
Explanation
Classify a triangle in a coordinate plane (continued)
PQO is a scalene triangle since none
of the sides are congruent.
Determine whether PQO with
vertices at P(-1, 2), Q(6, 3), O(0, 0),
is scalene, isosceles, or equilateral.
Explain.
Ex: Identify the indicated triangles in the figure.
a. isosceles triangles
Answer: ADE, ABE
b. scalene triangles
Answer: ABC, BCE, BDE, CDE, ACD, ABD
c. equilateral triangles
Answer: None!
Exit Slip
Is triangle A(0, 1), B(4, 4), and C(7,0)
scalene, isosceles or equilateral. Explain.
Answer:
AB = 5
BC = 5
CA = 7.1
Since AB = Triangle ABC is isosceles since two
of the sides are congruent.
Triangle Sum Theorem

The sum of the measures of the angles of
a triangle is 180°
x
y
x + y + z = 180
z
Find the missing angles.
1)
2)
x
26°
y
35°
31°
65°
3)
y°
x°
4)
82°
x°
70°
30°
1)80
2) 123
3) x = 60, y = 20
4) x = 57, y = 57, z = 82
41°
y°
z°
Example:

The measures of the angles of a triangle
are in the ratio 1:3:5. Find the measure of
each angle.
x + 3x + 4x = 180
8x = 180
x = 22.5
Plug in to find each angle:
1(22.5)= 22.5°
3(22.5) = 67.5°
4(22.5) = 90°
3x
x
4x