Parallel Lines and Transversals

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Parallel Lines and Transversals

• Geometry
• Chapter 3.3
• NCSCOS 2.02

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Essential Question

• What are the conclusions you get from
  intersections of two parallel lines by a
  transversal?

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Parallel Lines and Transversals
Objective Students will be able to solve for
missing angles using the properties of
transversals
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Angles and Parallel Lines Activity

• Using a ruler, trace over two of the parallel
  lines on your index card that are near the middle
  of the card and about an inch apart.
• Draw a transversal that makes clearly acute and
  clearly obtuse angles near the center of the card
• Label the angles with numbers from 1 to 8
• Sketch the parallel lines, transversal, and
  number labels in your notes. We will use this to
  record observations.

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Angles and Parallel Lines Activity

• Cut the index card carefully along the lines you
  first drew to make six pieces.
• Try stacking different numbered angles onto each
  other and see what you observe.
• Try placing different numbered angles next to
  each other and see what you Observe
• Mark your observations on the sketch in your
  notes

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Angles and Parallel Lines Activity

• Answer the following questions
• How many different sizes of angles where formed?
• 2
• What special relationships exist between the
  angles
• Congruent and supplementary
• Indicate the two different sizes of angles in
  your sketch.

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Angles and Parallel Lines Activity

• How can we use the vocabulary learned Friday, to
  describe these relationships?
• IF parallel lines are cut by a transversal, THEN
  
• corresponding angles are congruent (Postulate in
  Text)
• alternate interior angles are congruent (Theorem
  in Text)
• alternate exterior angles are congruent (Theorem
  in Text)
• Consecutive Interior angles are Supplementary
  (Theorem in Text)

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Perpendicular Transversal

• In your notes, trace over two of the parallel
  lines about one inch apart.
• Using a protractor, draw a line perpendicular to
  one of the parallel lines.
• Extend this perpendicular so that it crosses the
  other parallel line.
• Based on your observations in the previous
  exercise, what should be true about the new
  angles formed?
• Verify this with your protractor.
• If a line is perpendicular to one of two parallel
  lines, then it is perpendicular to the other.
  (Theorem in Text)

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Postulate 15 Corresponding Angles

• If two parallel lines are cut by a transversal,
  then the pairs of corresponding angles are
  congruent.

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Alternate interior Angles Theorem 3.4

• If two parallel lines are cut by a transversal,
  then the pairs of alternate interior angles are
  congruent.

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Same-Side Interior AnglesTheorem 3.5

• If two parallel lines are cut by a transversal,
  then the pairs of consecutive interior angles are
  supplementary. Measure of lt7 plus measure of lt8
  equals 180 degrees.

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Alternate Exterior AnglesTheorem 3.6

• If two parallel lines are cut by a transversal,
  then the pairs of alternate exterior angles are
  congruent.

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Perpendicular TransversalTheorem 3.7

• If a transversal is perpendicular to one of two
  parallel lines, then it is perpendicular to the
  other.

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Frayer Model
Alternate Exterior Angles
Alternate Interior Angles
Corresponding Angles
Consecutive Interior Angles