Page 1 of 6
4.1
Goal
Classify triangles by their
sides and by their angles.
Classifying Triangles
A triangle is a figure formed by three segments
joining three noncollinear points. A triangle
can be classified by its sides and
by its angles.
3 segments
3 noncollinear points
Key Words
• equilateral, isosceles,
scalene triangles
CLASSIFICATION OF TRIANGLES BY SIDES
SUMMARY
• equiangular, acute, right,
obtuse triangles
Equilateral
Triangle
Isosceles
Triangle
Scalene
Triangle
3 congruent sides
At least 2
congruent sides
No congruent sides
• vertex
1
EXAMPLE
Classify Triangles by Sides
Classify the triangle by its sides.
a.
b.
c.
4
4
4
Student Help
Equi- means “equal,”
and -lateral means
“side.” So, equilateral
means equal sides.
6
6
2
4
VOCABULARY TIP
4
3
Solution
a. Because this triangle has 3 congruent sides, it is equilateral.
b. Because this triangle has no congruent sides, it is scalene.
c. Because this triangle has 2 congruent sides, it is isosceles.
Classify Triangles by Sides
Classify the triangle by its sides.
1.
2
2.
8
3.
10
8
2
7
2
6
9
4.1
Classifying Triangles
173
Page 2 of 6
SUMMARY
CLASSIFICATION OF TRIANGLES BY ANGLES
Equiangular Triangle
Acute Triangle
3 congruent angles
3 acute angles
Right Triangle
Obtuse Triangle
1 right angle
IStudent Help
EXAMPLE
1 obtuse angle
Classify Triangles by Angles and Sides
2
ICLASSZONE.COM
MORE EXAMPLES
More examples at
classzone.com
Classify the triangle by its angles and by its sides.
a.
b.
c.
70
5
3
40
70
6.4
40
9
95 45
5.8
4
Solution
a. Because this triangle has 3 angles with measures less than 90 and
2 congruent sides, it is an acute isosceles triangle.
b. Because this triangle has a right angle and no congruent sides, it is
a right scalene triangle.
c. Because this triangle has one angle greater than 90 and no
congruent sides, it is an obtuse scalene triangle.
Classify Triangles by Angles and Sides
Classify the triangle by its angles and by its sides.
4.
5.
72
36
72
174
Chapter 4
Triangle Relationships
6.
6.2 60
70
7.6
50
7
30
30
120
Page 3 of 6
Student Help
VOCABULARY TIP
The plural of vertex is
vertices.
Point B is a vertex.
A vertex of a triangle is a
point that joins two sides of the
triangle. The side across from
an angle is the opposite side.
EXAMPLE
3
B
BC
&* is opposite aA.
A
C
Identify the Parts of a Triangle
Name the side that is opposite the angle.
a. aA
b. aB
c. aC
A
B
Solution
C
&* is the side that is opposite aA.
a. BC
&* is the side that is opposite aB.
b. AC
&* is the side that is opposite aC.
c. AB
4.1 Exercises
Guided Practice
Vocabulary Check
1. What is the difference between an obtuse triangle and an
acute triangle?
P
In Exercises 2–4, use the diagram.
2. Name the side opposite aP.
3. Name the side opposite aQ.
P
4. Classify the triangle by its sides.
Skill Check
R
Classify the triangle by its sides.
5.
6.
7.
7
5
7
7
4
6
Classify the triangle by its angles.
8.
9.
70
10.
40
70
4.1
Classifying Triangles
175
Page 4 of 6
Practice and Applications
Extra Practice
Classifying Triangles Classify the triangle by its sides.
See p. 681.
11.
12.
8
3
7
14.
13.
5
5
3
15.
5
16.
3
5
5
5
7
5
7
4
Classifying Triangles Classify the triangle by its angles.
17.
18.
28
19. 90
82
22
68
30
55
122
20.
43
21.
22.
65
55
60
23. Error Analysis A student claims
This triangle is
acute and obtuse.
that the triangle is both obtuse
and acute because it has an
obtuse angle and an acute
angle. What is wrong with
his reasoning?
30
130
20
Classifying Triangles Classify the triangle by its angles and by
its sides.
24.
25. E
B
26. L
M
120
59
A
Homework Help
59
Chapter 4
C
Triangle Relationships
28. T
N
F
D
P
27. P
Example 1: Exs. 11–16
Example 2: Exs. 17–41
Example 3: Exs. 42–47
176
62
42
42
U
29.
J
85
96
R
V
L
45
50
K
Page 5 of 6
Student Help
VISUAL STRATEGY
In Exs. 30–36 draw
a sketch with side
lengths or angle
measures that are
roughly correct, as
shown on p. 172.
Classify Triangles
EXAMPLE
Classify the triangle described.
a. Side lengths: 6, 8, 9
b. Angle measures: 50, 60, 70
Solution
You may want to sketch the triangle.
a.
b.
8
70
6
9
Because the triangle has three
sides with different lengths,
the triangle is scalene.
60
50
Because the triangle has three
angles with measures less than
90, the triangle is acute.
Matching Triangles In Exercises 30–36, use the example above to
match the triangle description with the most specific name.
30. Side lengths: 2 cm, 3 cm, 4 cm
A. Equilateral
31. Side lengths: 3 cm, 2 cm, 3 cm
B. Scalene
32. Side lengths: 4 cm, 4 cm, 4 cm
C. Obtuse
33. Angle measures: 60, 60, 60
D. Equiangular
34. Angle measures: 30, 60, 90
E. Isosceles
35. Angle measures: 20, 145, 15
F. Acute
36. Angle measures: 50, 55, 75
G. Right
Sports
Basketball The diagram shows the position and spacing of five
basketball players running the “triangle offense.”
37. What type of triangle is formed
by players A, B, and C?
38. What type of triangle is formed
by players C, D, and E?
39. What type of triangle is formed
by players B, D, and E?
A
40. Which three players appear
to form an obtuse triangle?
BASKETBALL The triangle
offense is used by many
professional teams. Players
are usually spaced 15 feet to
18 feet apart from each other.
This provides many options
for passing so a player can
make a basket.
B
41. Which three players appear
C
D
to form a scalene triangle?
E
4.1
Classifying Triangles
177
Page 6 of 6
Visualize It!
To help you determine
the side opposite a
vertex, you can draw
an arrow from the
vertex.
Identifying Parts of Triangles Identify which side is opposite
each angle.
42. A
43.
B
F
C
F
H
E
L
45.
E
44. G
D
G
FG
& is opposite aE.
46.
N
Visualize It!
R
P
T
Draw an example of the triangle.
48. obtuse scalene
49. right isosceles
50. acute scalene
51. right scalene
52. acute isosceles
53. obtuse isosceles
54. Multiple Choice Which of the following terms can be used to describe
a triangle with angle measures of 17, 17, and 146?
A
acute
B
right
C
F
H
&*
AB
&*
AC
G
J
D
obtuse
55. Multiple Choice What side is opposite aC?
Mixed Review
S
47.
P
K
M
Standardized Test
Practice
J
equiangular
A
C
&*
BC
&* and AC
&*
both BC
B
Complements and Supplements Find the value of each variable.
(Lesson 2.3)
56.
57.
58.
4x 8x (11x 7) (5x 3)
(6x 10)
50
2y Translations Find the image of the point using the translation
(x, y) → (x 2, y 4). (Lesson 3.7)
Algebra Skills
178
Chapter 4
59. (2, 5)
60. (1, 3)
61. (1, 2)
62. (0, 5)
63. (4, 2)
64. (0, 0)
65. (6, 4)
66. (3, 1)
Solving Equations Solve the equation. (Skills Review, p. 673)
67. 5x 15 180
68. x 2x 36 180
69. 3x 5x 20 180
70. 3x (x 8) 180
71. 2(x 1) 3x 7 180
72. 4(3x 1) 9x 10 180
Triangle Relationships