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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
• 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

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
• 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