Chapter 2 Lesson 5

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Chapter 2 Lesson 5

• Objective To prove and apply theorems about
  angles.

2
Theorem the statement that you prove true
Theorem 2-1 Vertical angles are congruent.
2
4
3
1
1 2 and
3 4
Paragraph proof written as sentences in a
paragraph
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Example 1
Write a paragraph proof.
Given 1 and 2 are vertical angles
1
3
2
Prove 1 2
Paragraph Proof By the Angle Addition Postulate,
m 1 m 3 180 and m 2 m
3 180. By substitution, m 1
m 3 m 2 m 3. Subtract m 3 from
each side. You get m 1 m
2.
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Example 2
Find the value of x.
4x
(3x35)
4x 3x 35 X 35
Vertical angles are congruent Subtract 3x from
each side
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Example 3
Theorem 2-2 Congruent Supplements Theorem If two
angles are supplements of the same angle (or of
congruent angles), then two angles are congruent
Given 1 and 2 are supplementary. 3
and 2 are supplementary.
2
1
Prove 1 3
3
Proof By the definition of supplementary angles,
m 1 m 2 180 and m 3
m 2 180. By substitution, m 1 m
2 m 3 m 2. Subtract m 2 from each
side. You get m 1 m 3.
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Theorem 2-3 Congruent Complements Theorem If two
angles are complements of the same angle (or of
congruent angles), then the two angles are
congruent. Theorem 2-4 All right angles are
congruent. Theorem 2-5 If two angles are
congruent and supplementary, then each is a right
angle.
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Homework
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