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To construct a parallel line, select the line AB, hold the shift key
down and select point C as well. Then, in the Construct menu choose
parallel line.
To measure the angle, select the three points, with the
vertex as your middle selection. Then, in the Measure menu, choose angle.
Record Your Data In a Table:
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You'll learn how to construct parallel
lines and discover some important relationships with an intersecting third line called a
transversal.
Sketch and Investigate
Construct a a line AB and a point C, not on the line.
Construct a line parallel to AB through point C.
Construct line CA. Drag points C and A to make sure
that all three lines are connected at those points..
Construct points D, E, F, G and H as
shown in the picture.
Use Sketchpad tomeasure the eight
angles that are formed in your figure. Be sure to be very systematic about your measuring
so that you don't measure the same angle twice.
Drag point A or B and see what happens to the angles.
Also drag the transversal CA. (Becareful not to drag the points and change the
order on your lines. That would change some angles into other angles.) Make and
record some of your observations.
When two parallel lines are crossed by a transversal,
pair of angles are formed (think back to FiVZiX OIL). These pairs of angles have specific
properties or a relationship they share.Complete the table below by first labelling the
second pair of each type of angle. Every "type" of angle has atleast two pairs,
but only one of the types has 4 pairs, see if you can determine which type it is. (hint:
Flip, turn, or rotate the letters from FiVZiX OIL to determine other pairs).
sg
Type of Angles |
Pair 1 |
Pair 2 |
Pair 3 |
Pair 4 |
Relationship |
| Corresponding |
ÐECA
& ÐBAH |
|
|
|
|
| Alternate Interior |
ÐECA
& ÐCAG |
|
|
|
|
| Alternate Exterior |
ÐFCD
& ÐBAH |
|
|
|
|
| Same-side Interior |
ÐDCA
& ÐGAC |
|
|
|
|
| Same-side Exterior |
ÐFCD
& ÐGAH |
|
|
|
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Points to Ponder . . .
Describe what you found out about Alternate Interior Angles
formed when two parallel lines are cut by a transversal.
___________________________________________________________
What about Corresponding Angles?
___________________________________________________________
What about Alternate Exterior Angles ?
___________________________________________________________
What about Same-side Exterior Angles ?
___________________________________________________________
What about Same-side Interior Angles ?
___________________________________________________________
If two lines are crossed by a transversal and the corresponding
angles, alternate interior angles, and alternate exterior angles are congruent, what can
you say about those lines ?
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