Basic Constructions
Constructing Parallel Lines
Given a line l and a point P not on l, construct a line through P, parallel to line l.
Step 1: Draw a line that goes through P
so that it intersects line l. Label this
point A.
Q
Next, we need to copy angle A at P.
P
B
A
Step 2: Opening your compass to any
comfortable position, set your compass
at A and make an arc that intersects both
sides of the angle. Label these points B
and C.
Put compass
point here
C
Put compass
point here
l
Step 3: Using the same opening, set
your compass at P and make an
identical mark. Where the arc
intersects the line from step 1, label
that point Q.
Given a line l and a point P not on l, construct a line through P, parallel to line l.
Put compass
point here
Q
P
Step 5: Using the same opening, set
your compass at Q and make an arc that
intersects the arc from step 3. Label this
point R.
Put compass
point hereR
B
A
Step 4: Set your compass at B and make
an arc that intersects line l at C.
Step 6: Draw PR
C
l
“If two lines are cut by a transversal
so that corresponding angles are
congruent, then the two lines are
parallel”
Therefore,
PR AC