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Activity
Lab
Activity Lab
Parallel Lines and Related Angles
Parallel Lines and
Related Angles
FOR USE WITH LESSON 3-1
Construct
Students will use geometry
software to investigate the
relationships among the eight
angles formed by parallel lines
and a transversal. By manipulating the lines and measuring
angles, they will discover the
postulates and theorems that
will be presented formally in
Lessons 3-1, 3-2, and 3-3.
Use geometry software to construct two parallel lines. Check that the lines
remain parallel as you manipulate them. Construct a point on each line. Then
construct the line through these two points. This line is called a transversal.
Investigate
Measure each of the eight angles formed
by the parallel lines and the transversal.
Record the measurements. Manipulate
the lines. Record the new measurements.
What relationships do you notice?
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2
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l2 O l4 O l6 O l8;
l1 O l3 O l5 O l7;
when a transversal
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1. When a transversal intersects parallel
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intersects two parallel
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lines, what are the relationships among
lines, the ' formed have
the angles formed? Make as
one of two measures;
many conjectures as possible.
' between n lines on the
opp. sides of the transversal are O; ' between the n lines
Extend
on the same side of the transversal are suppl.
2. Use your software to construct three or more parallel lines.
Construct a line that intersects all three lines. a-b. See below.
a. What relationships exist among the angles formed?
b. How many different angle measures are there?
Guided Instruction
EXERCISES
Using software enables students
to manipulate lines and measure
angles. They can observe that
parallel lines and a transversal
always have special angle
relationships and that when
alternate angles are congruent
or same-side interior angles are
supplementary, the lines must
be parallel.
3. Construct two parallel lines and a transversal
perpendicular to one of the parallel lines. What
angle does it make with the second parallel line?
a right l
4. Using geometry software, construct two lines and
a transversal, making sure that the two lines are
not parallel. Locate two angles that are on alternate
sides of the transversal and in the interior region
between the other two lines. Manipulate the lines
so that these angles have the same measure.
a. Make a conjecture as to the relationship between the two lines.
b. How is this conjecture different from the conjecture(s) you made in
Exercise 1? The other conjecture is the converse.
Tactile Learners
Students may see how many of
the activities they can complete
on paper using a protractor and
a straightedge.
Error Prevention!
Students who take a shortcut
and draw lines that appear
parallel may not observe the
angle relationships desired here.
In most software programs, it
is easy to draw horizontal and
vertical lines. Suggest that
students use parallel horizontal
lines or parallel vertical lines.
5. Again, draw two lines and a transversal, making sure that the two lines
are not parallel. Locate two angles that are on the same side of the
transversal and in the interior region between the two lines. Manipulate
the lines so that these angles are supplementary.
a. Make a conjecture as to the relationship between the two lines.
b. How is this conjecture different from the conjecture(s) you made in
Exercise 1? The other conjecture is the converse.
Resources
4a. If the ' between the
lines on alt. sides
of the transversal
are O, then the lines
are n.
5a. If the same-side
int. ' are suppl.,
then the lines are n.
6. Construct perpendicular lines a and b. At a point away from the intersection
of a and b, construct line c perpendicular to line a. Make a conjecture about
lines b and c. Lines b and c are n.
2a. Many of the ' are O to each other.
b. There are only two measures for all the ' formed.
Students may use any geometry
software program to explore
parallel lines and related angles.
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Activity Lab
Parallel Lines and Related Angles