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5–1
NAME
DATE
PERIOD
NAME
5–1
Study Guide
DATE
Classifying Triangles
Classifying Triangles
Triangles are classified in two different ways, either by their angles
or by their sides.
Classify each triangle by its angles and by its sides.
1.
60°
Classification of Triangles
Angles
Sides
all acute angles
scalene
no two sides congruent
obtuse
one obtuse angle
isosceles
at least two sides congrent
right
one right angle
equilateral
all sides congruent
35°
acute, equilateral
right, scalene
27 °
D
4 cm
20 cm
36°
11 m
30 cm
100°
22 cm
E
60°
M
n DEF is obtuse and scalene.
60°
isosceles, acute
N
n MNO is acute and equilateral.
7.
2. n XYZ, m/ X 5 60,
XY 5 YZ 5 ZX 5 3 cm
scalene, obtuse
8.
32°
130°
42°
9.
60°
18°
isosceles, acute
45°
60°
45°
60°
3. n DEF, m/ D 5 150,
DE 5 DF 5 1 inch
obtuse, scalene
acute, equilateral
isosceles, right
Z
L
F
Geometry: Concepts and Applications
D
K
M
X
right, scalene
4. n GHI, m/ G 5 30,
m/ H 5 45, GH 5 4 cm
Y
acute, equilateral
obtuse, isoceles
5. n NOP, m/ N 5 90,
NO 5 NP 5 2.5 cm
6. n QRS, m/ Q 5 100,
QS 5 1 inch,
QR 5 1}1} inches
P
I
G
R
10. right scalene
11. obtuse isosceles
12. right isosceles
13. right equilateral
2
obtuse,
scalene
not possible
O
right, isosceles
Q
© Glencoe/McGraw-Hill
Make a sketch of each triangle. If it is not possible to sketch the
figure, write not possible.
H
N
obtuse, scalene
E
179
S
Geometry: Concepts and Applications
© Glencoe/McGraw-Hill
180
Geometry: Concepts and Applications
(Lesson 5-1)
A2
Use a protractor and ruler to draw triangles using the given
conditions. If possible, classify each triangle by the measures
of its angles and sides.
1. n KLM, m/ K 5 90,
KL 5 2.5 cm, KM 5 3 cm
72° 72°
38°
60°
2.3 cm
102 °
6.
50°
11 m
isosceles, obtuse
5.
15 m
50°
40°
25 ft
Answers
5 cm
40°
4 cm
80°
51°
16 ft 100° 16 ft
5 cm
55°
6 in.
4.
Examples: Classify each triangle by its angles and by its sides.
O
F
1
2
3.
3 cm
60°
60°
acute
2.
6 in.
6 in.
PERIOD
Skills Practice
© Glencoe/McGraw-Hill
5–1
NAME
DATE
PERIOD
Practice
Classifying Triangles
wB
A
w, B
wC
w, w
AC
w
2. angles of the triangle
/A, /B, /ACB
/ACB
4. base angles
/A, /B
5. side opposite /BCA
DATE
PERIOD
wB
A
w
Key Terms
triangle a figure formed when three noncollinear points are
connected by segments
vertex of a triangle the vertex of an angle formed by two
adjacent segments of a triangle
acute triangle a triangle with all acute angles
obtuse triangle a triangle with one obtuse angle
right triangle a triangle with one right angle
scalene triangle (SKAY•leen) a triangle with no sides
congruent
isosceles triangle (eye•SAHS•uh•LEEZ) a triangle with at
least two sides congruent
equilateral triangle (EE•kwuh•LAT•ur•ul) a triangle with all
sides congruent
Reading the Lesson
1. Supply the correct numbers to complete each sentence.
2 acute angle(s), ______
0 right angle(s), and ______
1
a. In an obtuse triangle, there are ______
obtuse angle(s).
wC
A
w, w
BC
w
3 acute angle(s), ______
0 right angle(s), and ______
0
b. In an acute triangle, there are ______
obtuse angle(s).
7. angle opposite w
AC
w /B
2 acute angle(s), ______
1 right angle(s), and ______
0
c. In a right triangle, there are ______
obtuse angle(s).
2. Determine whether each statement is always, sometimes, or never true. If the statement is
not always true, explain why.
Classify each triangle by its angles and by its sides.
8.
a. A right triangle is scalene.
isosceles.
9.
Sometimes; a right triangle may be scalene or
Geometry: Concepts and Applications
b. An obtuse triangle is isosceles.
isosceles or scalene.
Sometimes; an obtuse triangle may be
c. An equilateral triangle is a right triangle.
all angles measuring 60°.
right, scalene
d. An equilateral triangle is isosceles.
Never; an equilateral triangle has
always
Helping You Remember
equiangular, equilateral
10. Find the measures of the legs of isosceles triangle ABC if
AB 5 2x 1 4, BC 5 3x 2 1, AC 5 x 1 1, and the perimeter of
nABC is 34 units. 14 units
© Glencoe/McGraw-Hill
181
Geometry: Concepts and Applications
3. A good way to remember a new mathematical term is to relate it to a nonmathematical
definition of the same word. How is the use of the word acute, when used to describe acute
pain, related to the use of the word acute when used to describe an acute angle or an acute
triangle? Sample answer: Both are related to the meaning of acute as
sharp. An acute pain is a sharp pain, and an acute angle can be
thought of as an angle with a sharp point. In an acute triangle, all of
the angles are acute.
© Glencoe/McGraw-Hill
182
Geometry: Concepts and Applications
(Lesson 5-1)
A3
6. congruent sides
Answers
3. vertex angle
NAME
Reading to Learn Mathematics
Classifying Triangles
For Exercises 1–7, refer to the figure at the right. Triangle ABC is
€ i A
isosceles with AB . AC and AB . BC. Also, XY
wB
w. Name each
of the following.
1. sides of the triangle
5–1