Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up 1. What are two angles whose sum is
90? 2. What are two angles whose sum is
180? 3. A part of a line between two points is
called a _________. 4. Two lines that intersect
at 90 are ______________.
complementary angles
supplementary angles
segment
perpendicular
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Problem of the Day Find the total number of
shaded triangles in each figure.
3 6 10
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Learn to classify triangles and solve problems
involving angle and side measures of triangles.
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Vocabulary
acute triangle obtuse triangle right
triangle congruent line segments scalene
triangle isosceles triangle equilateral triangle
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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.
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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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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.
E
D
F
Subtract the sum of the known angle measures from
180
So the measure of D is 90. Because DEF has
one right angle, the trophy is a right triangle.
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Check It Out Example 1
E
Sara designed this triangular trophy. The measure
of E is 22, and the measure of F is 22.
Classify the triangle.
D
F
Subtract the sum of the known angle measures 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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You can use what you know about vertical,
adjacent, complementary, and supplementary angles
to find the measures of missing angles.
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Additional Example 2A Using Properties of Angles
to Label Triangles Use the diagram to find the
measure of each indicated angle.
?QTR
?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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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.
180 123
57
33
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Check It Out Example 2A Use the diagram to find
the measure of each indicated angle.
?MNO
?MNO and ?PNO are supplementary angles, so the
sum of m? MNO and m?PNO is 180.
136
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Check It Out Example 2B
?MON
180 104
76
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Congruent line segments have the same length.
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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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
6.5 in.
6.5 in.
c 13 19.5
c 13 13 19.5 13
N
L
c 6.5
c
Side c is 6.5 inches long. Because LMN has
three congruent sides, it is an equilateral
triangle.
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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
7.2 in.
7.2 in.
d 14.4 16.6
d 14.4 14.4 16.6 14.4
C
A
d 2.2
d
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Insert Lesson Title Here
Lesson Quiz

• If the angles can form a triangle, classify the
  triangle as acute, obtuse, or right.
• 1. 37, 53, 90 2. 65, 110, 25
• 3. 61, 78, 41 4. 115, 25, 40
• The lengths of three sides of a triangle are
  given. Classify the triangle.
• 5. 12, 16, 25 6. 10, 10, 15

not a triangle
right
acute
obtuse
scalene
isosceles
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Lesson Quiz for Student Response Systems
1. If the following angles can form a triangle,
classify the triangle as acute, obtuse, or
right. 45?, 45?, 90? A. acute B. right
C. obtuse D. not a triangle
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Lesson Quiz for Student Response Systems
2. If the following angles can form a triangle,
classify the triangle as acute, obtuse, or
right. 40?, 90?, 60? A. acute B. right
C. obtuse D. not a triangle
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Lesson Quiz for Student Response Systems
3. If the following angles can form a triangle,
classify the triangle as acute, obtuse, or
right. 26?, 85?, 69? A. acute B. right
C. obtuse D. not a triangle
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Lesson Quiz for Student Response Systems
4. If the following angles can form a triangle,
classify the triangle as acute, obtuse, or
right. 36?, 100?, 44? A. acute B. right
C. obtuse D. not a triangle
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Lesson Quiz for Student Response Systems
5. The lengths of three sides of a triangle are
given. Classify the triangle. 8, 10, 12 A.
equilateral B. isosceles C. scalene
D. right
The lengths of three sides of a triangle are
given. Classify the triangle. 8, 10, 12
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Lesson Quiz for Student Response Systems
6. The lengths of three sides of a triangle are
given. Classify the triangle. 12, 8, 12 A.
equilateral B. isosceles C. scalene
D. right
The lengths of three sides of a triangle are
given. Classify the triangle. 8, 10, 12