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Splash Screen
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Lesson Menu
Five-Minute Check (over Lesson 41) Then/Now New
Vocabulary Theorem 4.1 Triangle Angle-Sum
Theorem Proof Triangle Angle-Sum
Theorem Example 1 Real-World Example Use the
Triangle Angle-Sum Theorem Theorem 4.2 Exterior
Angle Theorem Proof Exterior Angle
Theorem Example 2 Real-World Example Use the
Exterior Angle Theorem Corollaries Triangle
Angle-Sum Corollaries Example 3 Find Angle
Measures in Right Triangles
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5-Minute Check 1
Classify ?RST .
A. acute B. equiangular C. obtuse D. right

1. A
2. B
3. C
4. D

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5-Minute Check 2
A. 8 B. 10 C. 12 D. 14

1. A
2. B
3. C
4. D

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5-Minute Check 3
Find x if ?ABC is an equilateral triangle.
A. 2 B. 4 C. 6 D. 8

1. A
2. B
3. C
4. D

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5-Minute Check 4
A. ?ABC B. ?ACB C. ?ADC D. ?CAB

1. A
2. B
3. C
4. D

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5-Minute Check 5
Classify ?MNO as scalene, isosceles, or
equilateral if MN 12, NO 9, and MO 15.
A. scalene B. isosceles C. equilateral

1. A
2. B
3. C

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5-Minute Check 6
Which is not a classification for ?FGH?
A. acute B. scalene C. isosceles D. equiangular

1. A
2. B
3. C
4. D

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Then/Now
You classified triangles by their side or angle
measures. (Lesson 41)

• Apply the Triangle Angle-Sum Theorem.
• Apply the Exterior Angle Theorem.

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Vocabulary

• auxiliary line
• exterior angle
• remote interior angles
• flow proof

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Concept 1
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Concept 2
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Example 1
Use the Triangle Angle-Sum Theorem
SOFTBALL The diagram shows the path of the
softball in a drill developed by four players.
Find the measure of each numbered angle.
Understand Examine the information in the
diagram. You know the measures of two angles of
one triangle and only one measure of another. You
also know that ?1 and ?2 are vertical angles.
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Example 1
Use the Triangle Angle-Sum Theorem
Plan Find m?1 first because the measure of two
angles of the triangle are known. Use the
Vertical Angles Theorem to find m?2. Then you
will have enough information to find the measure
of ?3. Solve
Triangle Angle-Sum Theorem
Simplify.
Subtract 117 from each side.
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Example 1
Use the Triangle Angle-Sum Theorem
?1 and ?2 are congruent vertical angles. So, m?2
63.
Triangle Angle-Sum Theorem
Simplify.
Subtract 142 from each side.
Answer Therefore, m?1 63, m?2 63, and m?3
38. Check The sums of the measures of the
angles in each triangle should be 180. m?1 43
74 63 43 74 or 180?m?2 m?3 79 63
38 79 or 180?
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Example 1
Find the measure of ?3.
A. 95 B. 75 C. 57 D. 85

1. A
2. B
3. C
4. D

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Concept 3
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Concept 4
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Example 2
Use the Exterior Angle Theorem
GARDENING Find the measure of ?FLW in the fenced
flower garden shown.
m?LOW m?OWL m?FLW Exterior Angle
Theorem x 32 2x 48 Substitution 32
x 48 Subtract x from each side. 80 x Add
48 to each side.
Answer So, m?FLW 2(80) 48 or 112.
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Example 2
The piece of quilt fabric is in the shape of a
right triangle. Find the measure of ?ACD.
A. 30 B. 40 C. 50 D. 130

1. A
2. B
3. C
4. D

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Concept 5
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Example 3
Find Angle Measures in Right Triangles
Find the measure of each numbered angle.
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Example 3
Find Angle Measures in Right Triangles
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Example 3
Find Angle Measures in Right Triangles
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Example 3
Find m?3.
A. 50 B. 45 C. 85 D. 130

1. A
2. B
3. C
4. D

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End of the Lesson