Download Parallel Lines

Exploring Geometry
Geometer’s Sketchpad Activities
Parallel Lines
When two lines intersect they form four angles. The point of intersection of the lines is the vertex of all four
angles. In this activity, you’ll investigate relationships between pairs of these angles.
Sketch and Investigate
You'll learn how to construct parallel lines and discover some important relationships
with an intersecting third line called a transversal.
1. Construct a line AB and a point C, not on the line.
B
A
C
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
2. Construct a line parallel to AB through point C. Construct/label the
second point on this parallel line. Label it point D. This makes lines
AB & CD parallel (AB||CD).
3. Construct line CA. This line is called a transversal. Drag points C and
A to make sure that all three lines are connected at those points.
B
A
C
D
4. Construct points D, E, F, G and H as shown in the picture.
F
B
A
E
D
C
G
H
5. Use Sketchpad to measure 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.
6. 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.
GSP Parallel Linesr.doc, Created by S. Middleton
1
revised: 09/15/08
7. When two parallel lines are crossed by a transversal, several pairs of
angles are formed (think back to FiVZiX OIL). These pairs of angles
have specific names. Each name is based upon the location of the
angles in regards to which side of the transversal they are located on
(SAME or ALTERNATE) and based upon whether they are on the
INTERIOR or EXTERIOR of the parallel lines.
8. Complete the table below by first labeling the second pair of each type
of angle. Every "type" of angle has at least 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
Things to Do . . .
To measure an angle,
select three points. Make
sure that you select the
point you want to be the
vertex in the middle of your
selection. Then in
MEASURE menu, choose
ANGLE.
Use GSP to measure the distance from point D to each of the angle’s sides and the
angles that are formed.
• Measure the Corresponding Angles ∠EAF & ∠DCA and record them in the
table below:
• Measure the Alternate Interior Angles ∠EAC & ∠GCA and record them in
the table below:
• Measure the SAME-Side Interior Angles ∠EAF & ∠DCA and record them
in the table below:
• Find a second pair of each type of angle and repeat the process.
Type of Angles
Pair 1
Corresponding
∠EAF &
∠DCA
Alternate Interior
∠EAC &
∠GCA
Same-side
Interior
∠DCA &
∠EAC
Measurements
Pair 2
Measurements
Points to Ponder
Drag point F, H, D, or E to change the angles. How do the measures of the angles
compare?
• Write a conjecture, about the measures of the Corresponding Angles formed by
a transversal cutting across two parallel lines:
Repeat the process of dragging points F, H, D or E.
• Write a conjecture, about the measures of the Alternate Interior Angles formed by a transversal
cutting across two parallel lines:
GSP Parallel Linesr.doc, Created by S. Middleton
2
revised: 09/15/08