Name: ________________________________________
Date: ______________
Perpendicular Bisector Constructions
Period: ____
1) Constructing a Perpendicular Bisector/Midpoint of a Segment
Given: (line segment) AB
Regents:
Common Core:
Task: Bisect AB
Directions:
1. Place your compass point on A and stretch the compass MORE THAN half way to point B,
but not beyond B.
2. With this length, swing a large arc that will go BOTH above and below AB .
(If you do not wish to make one large continuous arc, you may simply place one small arc
above AB and one small arc below AB .)
3. Without changing the span on the compass, place the compass point on B and swing the arc
again. The two arcs you have created should intersect.
4. With your straightedge, connect the two points of intersection.
5. This new straight line bisects AB . Label the point where the new line and AB cross as C.
AB has now been bisected and AC = CB. (It could also be said that the segments are congruent, AC  CB )
Examples:
Name: ________________________________________
Date: ______________
Period: ____
2) Construct a Line Perpendicular to a Given Line Through a Given Point on the Line
Given: Point P is on a given line
Regents:
Common Core:
Task: Construct a line through P
perpendicular to the given line
Directions:
1. Place your compass point on P and sweep an arc of any size that crosses the line twice
(below the line). You will be creating (at least) a semicircle.
2. STRETCH THE COMPASS LARGER!!
3. Place the compass point where the arc crossed the line on one side and make a small arc
above the line.
4. Without changing the span on the compass, place the compass point where the arc crossed the line on the
OTHER side and make another arc. Your two small arcs should be crossing.
5. With your straightedge, connect the intersection of the two small arcs to point P.
This new line is perpendicular to the given line.
Examples:
Name: ________________________________________
Date: ______________
Period: ____
3) Construct a Line Perpendicular to a Given Line Through a Given Point off the Line
Given: Point P is off a given line (usually somewhere above the line)
Task: Construct a line through P
perpendicular to the given line
Regents:
Common Core:
Directions:
1. Place your compass point on P and sweep an arc of any size that crosses the line
twice.
2. Place the compass point where the arc crossed the line on one side and make an arc
ON THE OPPOSITE SIDE OF THE LINE.
3. Without changing the span on the compass, place the compass point where the arc
crossed the line on the OTHER side and make another arc. Your two new arcs should be
crossing on the opposite side of the line.
4. With your straightedge, connect the intersection of the two new arcs to point P.
This new line is perpendicular to the given line.
Examples:
Name: ________________________________________
Date: ______________
Perpendicular Bisectors - Homework
1) Given the following segments, construct a perpendicular bisector.
A
B
Period: ____
C
D
2) Construct a line perpendicular through a point on the line.
P
P
3) Construct a line perpendicular through a point off the line.
P
P
̅̅̅̅.
4) The diagram below shows the construction of the perpendicular bisector of 𝐴𝐵
Which statement is not true?
(1) AC = CB
(2) CB = ½ AB
(3) AC=2(AB)
(4) AC + CB = AB
Name: ________________________________________
5) Line segment AB is shown in the diagram below.
Date: ______________
Period: ____
Which two sets of construction marks, labeled I, II, III, and IV are part of the construction of the perpendicular
bisector of line segment AB?
(1) I and II
(2) I and III
(3) II and III
(4) II and IV
6) Two homes are built on a plot of land. Both homeowners have dogs, and are interested in putting up as much
fencing as possible between their homes on the land, but in a way that keeps the fence equidistant from each home.
Use your construction tools to determine where the fence should go on the plot of land.
7) Divide the following segment into 4 segments of equal length.