Parallel Lines and Transversals

1
Parallel Lines and Transversals

• Geometry
• Chapter 3, Section 3

2
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.

3
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

4
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.

5
Angles and Parallel Lines Activity

• How can we use the vocabulary learned yesterday,
  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)

6
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)