Geometer’s Sketchpad
5.3 Parallel lines
I.
1.
2.
3.
4.
5.
6.
Constructing Parallel Lines
Plot two points in the field, one the left and one on the right. Label the one on the
left “A” and the right “B”
Select both points. From the top menu select “Construct” and “line” from the
drop-down menu. Try to get it so that the line is approximately horizontal.
Above the line plot a third point labeled “C”
Select the line AB and the point C. From the top menu select “Construct” and
“Parallel Line” from the drop-down menu. Move the points around to see that it
will always parallel the line AB.
Select A and C and construct a segment joining the two points. Select the
segment. From the top menu select “Measure” and “Length” from the drop-down
menu.
AC = _______
Select the points C, A, and B in that order. From the top menu select “Measure”
and “Angle” from the drop-down menu.
m∠CAB = ___________
7. Select the point C. Using the left and right arrow keys only, move C without
moving the line. Move the point so that the segment is as small a length as
possible:
AC = _______
m∠CAB = ___________
What angle seems to minimize the segment length?
8. Select the point tool from the tool bar.
. Mark a point on the line that point C
is on. Label it as “D”
9. Construct a segment from D to B. Find the measure of the segment as well as
the measure of ∠ABD.
BD = _______
m∠ABD = ___________
10. Using the arrow keys to move only the point D, try to minimize the distance
between D and B.
BD = _______
m∠ABD = ___________
What do you notice about the segments AC and BD?
Theorem 5-8
If two lines are parallel,
II.
Multiple Parallel Lines
1. Select the segment AC. From the top menu select “Construct” and “Midpoint from
the drop-down menu. Label the midpoint as “E”
2. Construct a parallel line through E to line AB.
3. Select the points A and E. From the top menu select “Measure” and “Distance”
from the drop-down menu. Do the same for the points E and C.
AE = _______
EC = ________
4. Move the lines around and verify that the values stay the same.
5. Select the segment BD and the new parallel line. From the top menu select
“Construct” and “Intersection” from the drop-down menu. Label the intersection
“F”
6. Find the distance BF and FD.
BF = _______
FD = ________
What do notice?
Move the segment BD around. What can you conclude?
Theorem 5-9
If three parallel lines
The point F is the _____________ of BD.
Theorem 5-10
A line that contains
III.
Midpoint lines
1. Open a new sketch.
2. Construct a triangle and label the vertices.
3. Find the midpoint of side AB and label it D.
4. Do the same for BC and label the midpoint E
5. Construct a segment joining D and E.
6. Find the measure of AC and DE .
AC = _______ and DE = _______
What do you notice?
Move your triangle so that the distances are different. What are the new
measures?
AC = _______ and DE = _______
What can you conclude?
7. Do the two lines appear to be parallel? How could you prove that fact?
8. Measure the angle BED by selecting in order Point B, E, and D. From the top
bar select “Measure” and “Angle” from the drop-down menu.
9. Measure the angle BCA.
mBED  _________
mBCA  _________
What can you conclude?
Theorem 5-11
The segment that joins the midpoints of two sides of triangle is…
(1)
and
(2)
10. Find the midpoint of AC and label it F. Construct the segments DF and EF
How many pairs of parallel lines are there in your diagram now? State them:
How many triangles have been formed from the original triangle?
What might be true about these triangles?
How could you check that?
Check if ADF  FEC and BDE  FED
11. Complete the statement:
Segments that join the 3 midpoints of the side of a triangle ….
Exercises
B
S
T
A
U
C
1.
a. Complete the following chart given that S,T, and U are midpoints.
AB
12
BC
14
15
AC
18
22
10
b. Name the segments congruent to AU .
c. Name the angles congruent to UST .
2. Given: AR || BS || CT ; RS  ST
a. If RS = 12, then ST = ____
b. If AB = 8, then BC = ____
c. If AC = 20, then AB = ____
d. If AC = 10x, then BC = ____
ST
TU
SU
10
9
7.8