Constructing Parallel Lines – Step by Step Guide
Step 1: Using a straight edge, draw a horizontal line. On this line put tow points P and Q.
P
Q
Step 2: Draw a diagonal line that goes through point P (approximately a 45 degree angle) Along this new line,
add a point R.
R
P
Q
Step 3: Using a compass, draw an arc, from point P, that is approximately half way to point R. Where the arc
crosses PR and PQ, label a point S. DO NOT MOVE THE COMPASS AFTER MAKING THIS ARC!
R
S
P
Q
Step 4: Put the compass at point R. Repeat the arc that goes through PR and an imaginary line parallel to PQ.
Label the point where the arc crosses PR as point T.
T
R
S
P
CONTINUE ON BACK
Q
Step 5: Take the compass and put the endpoint at point S. Draw an arc that has radius SU and marks the
intersection between arc SU and PQ. DO NOT MOVE THE COMPASS AFTER MAKING THIS MARK.
T
R
S
P
U
Q
Step 6: With the compass at the same distance as you mark you used in Step 5, put the compass end at point T.
Draw another arc that goes below line PT and label this intersection point X.
T
R
X
S
P
U
Q
Step 7: Draw a straight line that goes through points R and X. You have now constructed parallel lines.
T
R
X
S
P
U
Q
Step 8: Use the corresponding angles postulate and a protractor to check if lines RX and PQ are parallel.
Explain how you know that you have constructed parallel lines.