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NAME
DATE
4-1
PERIOD
Study Guide and Intervention
Classifying Triangles
Classify Triangles by Angles One way to classify a triangle is by the measures
of its angles.
If all three of the angles of a triangle are acute angles, then the triangle is an acute triangle.
•
If all three angles of an acute triangle are congruent, then the triangle is an equiangular triangle.
•
If one of the angles of a triangle is an obtuse angle, then the triangle is an obtuse triangle.
•
If one of the angles of a triangle is a right angle, then the triangle is a right triangle.
Example
a.
Lesson 4-1
•
Classify each triangle.
A
60°
B
C
All three angles are congruent, so all three angles have measure 60°.
The triangle is an equiangular triangle.
E
b.
120°
35°
D
25°
F
The triangle has one angle that is obtuse. It is an obtuse triangle.
c.
G
90°
H
60°
30°
J
The triangle has one right angle. It is a right triangle.
Exercises
Classify each triangle as acute, equiangular, obtuse, or right.
2. N
1. K
30°
67°
30°
O
3.
Q
60°
120°
L
90°
23°
4.
P
M
R
5.
T
W
60°
60°
S
B
6.
60°
45°
50°
U
65°
Chapter 4
65°
V
X
90°
45°
5
Y
F
28°
92°
D
Glencoe Geometry
NAME
DATE
4-1
PERIOD
Study Guide and Intervention
(continued)
Classifying Triangles
Classify Triangles by Sides You can classify a triangle by the number of congruent sides. Equal
numbers of hash marks indicate congruent sides.
•
If all three sides of a triangle are congruent, then the triangle is an equilateral triangle.
•
If at least two sides of a triangle are congruent, then the triangle is an isosceles triangle.
Equilateral triangles can also be considered isosceles.
•
If no two sides of a triangle are congruent, then the triangle is a scalene triangle.
Example
a.
Classify each triangle.
b.
H
c.
N
T
23
L
R
J
Two sides are congruent.
The triangle is an
isosceles triangle.
X
P
All three sides are
congruent. The triangle
is an equilateral triangle.
12
V
15
The triangle has no pair
of congruent sides. It is a
scalene triangle.
Exercises
Classify each triangle as equilateral, isosceles, or scalene.
1.
2.
A
2
G
4.
18
1
C
K
18
Q
I
32x
8x
C
W
17
12
18
5. B
S
M
3.
G
x
6. D
A
x
32x
O
19
E
x
F
U
7. ALGEBRA Find x and the length of each
side if RST is an equilateral triangle.
8. ALGEBRA Find x and the length of
each side if ABC is isosceles with
AB = BC.
B
R
5x – 4
2x + 2
S
Chapter 4
3x
4y
3y + 2
T
A
6
3y
C
Glencoe Geometry