Sec 2'7 Prove Angle Pair Relationships

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Sec 2.7 Prove Angle Pair Relationships
Theorem 2.3 Right Angles Congruence Thm All
right angles are congruent. Theorem 2.4
Congruent Supplements Theorem If two angles are
supplementary to the same angle (or to congruent
angles), then they are congruent.
If ?1 and ?2 are supplementary and ?3 and ?2 are
supplementary, then ?1 ? ?3
2
1
3
2
EXAMPLE 1
Use right angle congruence
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Theorem 2.5 Congruent Complements Theorem
If two angles are complementary to the same angle
(or to congruent angles), then they are congruent.
If ?4 and ?5 are complementary and ?6 and ?5 are
complementary, then ?4 ? ?6
5
4
6
4
EXAMPLE 2
5

• When two lines intersect, pairs of vertical
  angles and linear pairs are formed.

Postulate 12 Linear Pair Postulate If two
angles form a linear pair, then they are
supplementary.
?1 and ?2 form a linear pair, so ?1 and ?2 are
supplementary and m?1 m?2 180º
2
1
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Theorem 2.6 Vertical Angles Congruence Theorem
Vertical angles are congruent.
2
?1 ? ?3, ?2 ? ?4
3
1
4
7
EXAMPLE 3
8
for Example 3
GUIDED PRACTICE
9
for Example 3
GUIDED PRACTICE
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EXAMPLE 4
32 (3x 1) 180
Original equation
32 3x 1 180
Distributive property of equality
3x 147
Subtract 33 from each side
x 49
Divide each side by 3
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Bookwork p. 127-129 6, 8-12all, 15-28all,
37,38