Download PreCalculus AB

Honors Geometry
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Name
Investigation with Parallel Lines and Associated Angles
SKETCHPAD
1.
Using Sketchpad, draw two lines which are not parallel, and draw a third line
which crosses these two. (The third line is called a transversal.)
2.
Construct enough points (8) to label all of the angles shown. (Note that your
angles will not be called < 1,<2, <3, etc..)
(Note: Use the point tool to place a point on the lines. Use the text tool to label
the points. If the points are not labeled as above, you can double click on the
label and a box will pop up and you can rename the points.)
3.
Measure all 8 angles, and record your results below.
4.
Record 3 sets of measurements. (Record a set, move one of the lines, record
measurements again, move one line, and record the measurements again.
m< 1 =
m< 2 =
m< 3 =
m< 4 =
m< 5 =
m< 6 =
m< 7 =
m< 8 =
5.
m< 1 =
m< 2 =
m< 3 =
m< 4 =
m< 5 =
m< 6 =
m< 7 =
m< 8 =
m< 1 =
m< 2 =
m< 3 =
m< 4 =
m< 5 =
m< 6 =
m< 7 =
m< 8 =
Save your Sketchpad document as NONPARALLEL. I may ask to see your
document in class.
Parallel/Non Parallel Lines & Angles Investigation
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6.
Using Sketchpad, construct ABD first. Mark points A, B, and D on the line.
Choose a point H which is not on AB , using the point tool. Construct segment
CBHF (Highlight A and C, and construct a line.). By the way, I am following
the drawing above. Choose H and ABD , and construct a line through H parallel
to ABD . Construct other points in the drawing above. (You can extend the line
segments, or you can make them into lines, if necessary, in order to name all
angles with three letters, as Sketchpad requires you to do. You cannot use the
numbered names for angles in Sketchpad.
7.
Measure all of the angles three times, as you did in the investigation above.
m< 1 =
m< 2 =
m< 3 =
m< 4 =
m< 5 =
m< 6 =
m< 7 =
m< 8 =
m< 1 =
m< 2 =
m< 3 =
m< 4 =
m< 5 =
m< 6 =
m< 7 =
m< 8 =
m< 1 =
m< 2 =
m< 3 =
m< 4 =
m< 5 =
m< 6 =
m< 7 =
m< 8 =
8.
Save your Sketchpad document as PARALLELS.
10.
QUESTIONS:
a)
Are there any congruent angles? If so, which ones?
b)
Are there any supplementary angles? If so, which ones?
c)
Are there any complementary angles? If so, which ones?
NEW DEFINITIONS.
Parallel/Non Parallel Lines & Angles Investigation
page 3
A transversal is a line which intersect two other lines.
When a transversal intersects two lines, then four of the angles are on the “outside” of the
two lines. They are called exterior angles. (In the drawing, < 1, <2, <7, and<8 are
exterior angles.)
When a transversal intersects two lines, then four of the angles are on the “inside” of the
two lines. They are called interior angles. . (In the drawing, < 3, <4, <5, and<6 are
exterior angles.)
When a transversal intersects two lines, corresponding angles are a pair of angles so that
one is an interior angle and the other is an exterior angle. They lie on the same side of
the transversal.
When a transversal intersects two lines, alternate interior angles are a pair of angles so
that both are interior angles. They lie on the opposite side of the transversal.
When a transversal intersects two lines, alternate exterior angles are a pair of angles so
that both are exterior angles. They lie on the opposite side of the transversal.
When a transversal intersects two lines, same side interior angles are a pair of angles so
that both are interior angles. They lie on the same side of the transversal.
When a transversal intersects two lines, same side exterior angles are a pair of angles so
that both are exterior angles. They lie on the same side of the transversal.
11.
Look at your two investigations above----one with non parallel lines cut by a
transversal, and the other with parallel lines cut by a transversal.
See if there are some conclusions that appear to be true (conjectures).
Angles
With non-parallel lines
With parallel Lines
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corresponding
alternate interior
alternate exterior
same-side interior
same-side exterior
Parallel/Non Parallel Lines & Angles Investigation
12.
State these conjectures in the IF … THEN … format
If lines are parallel and cut by a transversal, then corresponding angles are
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Add other similar statements……
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