Download Triangles

LES
SO
N
Triangles
Goal: Classify triangles.
Vocabulary
Acute triangle:
An acute triangle has three acute angles.
Right triangle:
A right triangle has one right angle.
Obtuse triangle:
An obtuse triangle has one obtuse angle.
Congruent sides are sides that have the same
length.
Congruent sides:
Equilateral triangle:
Isosceles triangle:
Scalene triangle:
EXAMPLE
1
An equilateral triangle has three congruent
sides.
An isosceles triangle has at least two congruent
sides.
A scalene triangle has no congruent sides.
Finding an Angle Measure in a Triangle
Find the value of x in the triangle shown.
Triangles are
named by their
vertices. The vertices
of the triangle in
Example 1 are L, M,
and N, so the triangle
can be named with the
notation LMN. This
notation is read
"triangle LMN."
x 75 28 180 x 103 180
x 77
L
Sum of angle measures
in a triangle is 180 .
28
Add 75 and 28 .
Subtract 103 from
each side.
75
x
M
N
Answer: The value of x is 77 .
Lesson 10.3
Triangles
| 217
EXAMPLE
2
Finding the Measure of an Exterior Angle
Find the value of y in the figure.
70
To find the value of y, use the fact that
adjacent interior and exterior angles of a
triangle are supplementary.
y 49 180 y 131
y 49
61
Definition of supplementary angles
Subtract 49 from each side.
Answer: The value of y is 131 .
Guided Practice
1.
Find the value of y.
y
50
2.
62
80
28
y
50
EXAMPLE
3
152
Classifying a Triangle by Angle Measures
Classify the triangle by its angle measures.
35
The triangle has one right angle, so it
is a(n) right triangle.
218
|
Chapter 10
Notetaking Guide
55
EXAMPLE
4
Standardized Test Practice
Which statement about the triangle is true?
A It is scalene.
B It is equilateral.
5 cm
5 cm
C It is isosceles.
D Its 3 angles are congruent.
2 cm
Solution
The triangle is not scalene because two sides are congruent. The triangle
is not equilateral because only two sides are congruent. The triangle is
isosceles because two sides are congruent. The triangle does not have
three congruent angles because it is not equilateral .
Answer: The correct answer is C .
A
B
D
Classify the triangle by its angle measures.
Guided Practice
3.
4.
5.
29
50
C
21
39
101
72
87
51
obtuse
right
acute
Classify the triangle by the lengths of its sides.
6.
7.
8 cm
8.
4 in.
10 m
6 cm
5 cm
3 in.
10 m
4 in.
10 m
scalene
isosceles
equilateral and
isosceles
Lesson 10.3
Triangles
| 219