3'2 Angles and Parallel Lines 102808

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3.2 Angles and Parallel Lines 10/28/08

• Corresponding Angles Postulate
• If two parallel lines are cut by a transversal,
  then each pair of corresponding angles is
  congruent.

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1
3
4
6
5
7
8
2
Theorems

• Alternate Interior Angles Theorem
• If two parallel lines are cut by a transversal,
  then each pair of alternate interior angles is
  congruent.
• Consecutive Interior Angles Theorem
• If two parallel lines are cut by a transversal,
  then each pair of consecutive interior angles is
  supplementary.
• Alternate Exterior Angles Theorem
• If two parallel lines are cut by a transversal,
  then each pair of alternate exterior angles is
  congruent.
• Perpendicular Transversal Theorem
• In a plane, if a line is perpendicular to one of
  two parallel lines, then it is perpendicular to
  the other.

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Proof Theorem 3.4

• Given p q, t p
• Prove t q

t
p
1
2
q
4

• Statements
• 1. p q, t p
• 2. is a right angle
• 3.
• 4.
• 5.
• 6.
• 7. is a right angle
• 8.

• Reasons
• 1. Given
• 2. Definition of perpendicular lines
• 3. Definition of right angles
• 4. Corresponding Angles Postulate
• 5. Definition of congruent angles
• 6. Substitution Property
• 7. Definition of right angles
• 8. Definition of perpendicular lines

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Find Values of Variables

• If

1
F
3
E
G
2
4
H
6

• Find x.
• Find y.