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8-5
8-5 Triangles
Triangles
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
8-5 Triangles
Warm Up
1. What are two angles whose sum is
90°? complementary angles
2. What are two angles whose sum is
180°? supplementary angles
3. A part of a line between two points is
called a _________.
segment
4. Two lines that intersect at 90° are
______________.
perpendicular
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8-5 Triangles
Problem of the Day
Find the total number of shaded
triangles in each figure.
3
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6
10
8-5 Triangles
Learn to classify triangles and solve
problems involving angle and side
measures of triangles.
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8-5 Triangles
Vocabulary
acute triangle
obtuse triangle
right triangle
scalene triangle
isosceles triangle
equilateral triangle
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8-5 Triangles
A triangle is a closed figure with three line
segments and three angles. Triangles can be
classified by the measures of their angles. An
acute triangle has only acute angles. An obtuse
triangle has one obtuse angle. A right triangle
has one right angle.
Acute triangle
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Obtuse triangle
Right triangle
8-5 Triangles
To decide whether a triangle is acute, obtuse,
or right, you need to know the measures of
its angles.
The sum of the measures of the
angles in any triangle is 180°. You
can see this if you tear the
corners from a triangle and
arrange them around a point on a
line.
By knowing the sum of the measures of
the angles in a triangle, you can find
unknown angle measures.
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8-5 Triangles
Additional Example 1: Application
Sara designed this triangular trophy. The
measure of E is 38°, and the measure
of F is 52°. Classify the triangle.
To classify the triangle, find the
measure of D on the trophy.
m
D = 180° – (38° + 52°)
E
D
F
D = 180° – 90° Subtract the sum of the
known angle measures
m D = 90°
from 180°
So the measure of D is 90°. Because DEF has
one right angle, the trophy is a right triangle.
m
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8-5 Triangles
Check It Out: Example 1
Sara designed this triangular trophy. The
measure of E is 22°, and the measure
of F is 22°. Classify the triangle.
To classify the triangle, find the
measure of D on the trophy.
m
E
D
F
D = 180° – (22° + 22°)
m D = 180° – 44° Subtract the sum of the
known angle measures
m D = 136°
from 180°
So the measure of D is 136°. Because DEF has
one obtuse angle, the trophy is an obtuse triangle.
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8-5 Triangles
You can use what you know about
vertical, adjacent, complementary, and
supplementary angles to find the
measures of missing angles.
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8-5 Triangles
Remember!
Vertical angles are congruent. The sum
of the measures of complementary
angles is 90°. The sum of the measures
of supplementary angles is 180°.
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8-5 Triangles
Additional Example 2A: Using Properties of
Angles to Label Triangles
Use the diagram to find the measure of each
indicated angle.
Q
QTR
P
QTR and STR are
supplementary angles, so the
sum of mQTR and mSTR is
180°.
mQTR = 180° – 68°
= 112°
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T
68°
R
55°
S
8-5 Triangles
Additional Example 2B: Using Properties of
Angles to Label Triangles
 QRT
 QRT and SRT are
complementary angles, so the
sum of mQRT and mSRT is
90°.
m SRT = 180° – (68° + 55°)
= 180° – 123°
= 57°
m
QRT = 90° – 57°
= 33°
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Q
P
T
68°
R
55°
S
8-5 Triangles
Check It Out: Example 2A
Use the diagram to find the measure of each
indicated angle.
MNO
M
MNO and PNO are
N
supplementary angles, so the
sum of m MNO and mPNO
is 180°.
m
MNO = 180° – 44°
= 136°
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L
44°
O
60°
P
8-5 Triangles
Check It Out: Example 2B
MON
MON and PON are
complementary angles, so the
sum of m MON and m PON
is 90°.
m
m
MON = 90° – 76°
L
N
PON = 180° – (44° + 60°)
= 180° – 104°
= 76°
= 14°
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M
44°
O
60°
P
8-5 Triangles
Triangles can be classified by the lengths
of their sides. A scalene triangle has no
congruent sides. An isosceles triangle
has at least two congruent sides. An
equilateral triangle has three congruent
sides.
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8-5 Triangles
Additional Example 3: Classifying Triangles by
Lengths of Sides
Classify the triangle. The sum of the lengths
of the sides is 19.5 in.
M
c + (6.5 + 6.5) = 19.5
c + 13 = 19.5
6.5 in.
6.5 in.
c + 13 – 13 = 19.5 – 13
c = 6.5
L
c
N
Side c is 6.5 inches long. Because LMN has
three congruent sides, it is an equilateral triangle.
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8-5 Triangles
Check It Out: Example 3
Classify the triangle. The sum of the lengths
of the sides is 15.6 in.
B
d + (7.2 + 7.2) = 16.6
d + 14.4 = 16.6
7.2 in.
7.2 in.
d + 14.4 – 14.4 = 16.6 – 14.4
d = 2.2
A
d
C
Side d is 2.2 inches long. Because ABC has
two congruent sides, it is an isosceles triangle.
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8-5 Triangles
Insert Lesson Title Here
Lesson Quiz
If the angles can form a triangle, classify the
triangle as acute, obtuse, or right.
not a
1. 37°, 53°, 90° right 2. 65°, 110°, 25°
triangle
3. 61°, 78°, 41° acute 4. 115°, 25°, 40° obtuse
The lengths of three sides of a triangle are
given. Classify the triangle.
5. 12, 16, 25 scalene
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6. 10, 10, 15
isosceles