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Parallel Lines and Transversals

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Parallel Lines and Transversals Geometry Chapter 3.3 NCSCOS: 2.02 Essential Question: What are the conclusions you get from intersections of two parallel lines by a ... – PowerPoint PPT presentation

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Title: Parallel Lines and Transversals


1
Parallel Lines and Transversals
  • Geometry
  • Chapter 3.3
  • NCSCOS 2.02

2
Essential Question
  • What are the conclusions you get from
    intersections of two parallel lines by a
    transversal?

3
Parallel Lines and Transversals
Objective Students will be able to solve for
missing angles using the properties of
transversals
4
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5
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.

6
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7
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

8
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9
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.

10
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)

11
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)

12
Postulate 15 Corresponding Angles
  • If two parallel lines are cut by a transversal,
    then the pairs of corresponding angles are
    congruent.

13
Alternate interior Angles Theorem 3.4
  • If two parallel lines are cut by a transversal,
    then the pairs of alternate interior angles are
    congruent.

14
Same-Side Interior Angles Theorem 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.

15
Alternate Exterior Angles Theorem 3.6
  • If two parallel lines are cut by a transversal,
    then the pairs of alternate exterior angles are
    congruent.

16
Perpendicular Transversal Theorem 3.7
  • If a transversal is perpendicular to one of two
    parallel lines, then it is perpendicular to the
    other.

17
Frayer Model
Alternate Exterior Angles
Alternate Interior Angles
Corresponding Angles
Consecutive Interior Angles
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