DIRECTIONS FOR CONSTRUCTIONS
1.
Angle Bisector
a.
b.
c.
d.
e.
f.
g.
2.
Put your pointer of compass and open your compass more than ½ of rays of angle A and
make a ½ circle.
Label B and C where the arc crosses rays of angle A.
Put the compass point on C and make an arc between the rays of angle A.
Put the compass point on B and make an arc between the rays of angle B.
The two arcs drawn from points B and C should form an “X”.
Label D the intersection of the two arcs.
Connect A to D and this is you Angle Bisector.
Perpendicular Bisector (*MIDPOINT)
a. Put your compass point on A and open your compass more than ½ of line segment AB.
b. Make a ½ circle.
c. Put your compass point on B and using the same distance from point A, make a ½ circle. (it
should look like a tear drop)
d. Label the points of intersection of the two ½ circles with a C and D.
e. Connect C to D and this is your Perpendicular Bisector that also find your midpoint of line
segment AB and makes a right angle (90 degrees).
3. Perpendicular Line from a Point on the Line
a. You start with a Line and a point that we will call P on the line.
b. Draw a circle with P as the center of the circle.
c. Label A and B where the circle intersects the line.
d. Follow directions for the perpendicular bisector in #2 above,
4.
A perpendicular from a Point off a Line (*ALTITUDE)
a. You will start with a Line and a point that we will call P above the line.
b. Put your compass point on P and open it about ½-inch past the line and draw a ½ circle.
c. Label A and B where the ½ circle intersects the line.
d. Follow directions for the perpendicular bisector in #2 above.
5.
Construct an Angle Congruent to a Given Angle
a. Put your compass point on point A and open compass more than half the rays of angle A.
b. Make a ½ a circle.
c. Mark points B and C where the arc crosses angle A.
d. With the compass the same distance, put the compass point on A’ and make a half circle.
e. Mark C’ where arc meets ray A’.
f. With the compass go back to arc BC and measure the arc distance from point C to point B.
g. Using the arc BC distance put compass point on C’ and make a ¼ circle that should intersect
the arc.
h. Label the point of intersection B’.
i. Draw in Ray A’B’. (which is the other ray of the new angle A’).
6. Construct a line Parallel to a Given Line at a Given Point
a. Draw a transversal through the given point that intersects the given line.
b. Label the given point A’ and label point A where the transversal intersects the line.
c. Put your compass point on point A and open compass more than ½ the rays of angle A.
d. Make a ½ circle.
e. Mark points B and C where the arc crosses angle A.
f. With the compass the same distance, put the compass on A’ and make a ½ circle.
g. Mark B’ where arc meets ray A’.
h. With the compass go back to arc BC and measure the arc distance from point C to point B.
i. Using the arc BC distance put compass point on B’and make a ¼ circle that should intersect
the arc.
j. Label the point of intersection C’.
k. Draw in Ray A’C’. (which is the other ray of the new angle A’ that is also the parallel line to
AC). Note: You just copied an angle from point A to A’ that are congruent corresponding angles that
make AC and A’C’ parallel to each other.
7. Construct a Triangle Using Side Lengths
a. Label each line segment “a”, “b” and “c”.
b. Draw a line segment a little bit longer than the largest line segment (leave some space to
construct a triangle above the line segment).
c. Label the left side of the line segment A.
d. With compass measure off the distance of the longest segment and put your compass point
on A and make a some arc so that it intersects the line segment you drew.
e. Label the intersection with a B.
f. Measure line segment “b” off with the compass.
g. Using the distance of “b”, put the compass point on A and make a ¼ of a circle.
h. Measure line segment “a” off with compass.
i. Using the distance of “a”, put the compass point on B and make a ¼ of a circle.
j. Where the 2 ¼ of a circles intersect, mark that with a C.
k. Now connect A to B and B to C and you have your triangle.
8. Construct an Equilateral Triangle Using a Circle
a. Draw a Circle with at least a 1-inch radius that fits on your note sheet.
b. Find any starting point on your circle and make a small tick mark.
c. Keeping you compass set at the radius that you drew your circle with, put your point of your
compass on your tick mark and mark your radius distance around your circle with small tick marks until
you come back to your starting point. Note: Be sure not to move your compass!!! You should have six
tick marks when you are done.
d. Mark every other tick mark with a point and connect them to form an equilateral triangle
with 60 degree angles.