Download Parallel Lines and Transversals

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
transversal?
– Parallel Lines and Transversals
Objective: Students will be able to solve for missing
angles using the properties of transversals
4
Angles and Parallel Lines Activity
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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.
Angles and Parallel Lines Activity
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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
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.
Angles and Parallel Lines Activity
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How can we use the vocabulary learned Friday, to
describe these relationships?
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IF parallel lines are cut by a transversal, THEN
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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)
Perpendicular Transversal
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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)
Postulate 15: Corresponding Angles
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are
congruent.
2
1
1  2
Alternate interior Angles
Theorem 3.4
If two parallel lines are cut by a transversal,
then the pairs of alternate interior angles are
congruent.
3
4
3  4
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 <7 plus
measure of <8 equals 180 degrees.
7
8
7 + 8 = 180
Alternate Exterior Angles
Theorem 3.6
If two parallel lines are cut by a transversal,
then the pairs of alternate exterior angles are
congruent.
5
6
5  6
Perpendicular Transversal
Theorem 3.7

If a transversal is perpendicular to one of two
parallel lines, then it is perpendicular to the
other.
Frayer Model
Alternate Exterior Angles
Corresponding Angles
Alternate Interior Angles
Consecutive Interior Angles