Download Directions for constructing a Perpendicular Bisector can be found

MAZZEO/PRIZIO
GEOMETRY Period__Date__/__/__Name______________________________
Lesson 3.1 How do we construct a perpendicular bisector and construct an inscribed square?
Do
BREAKING NEWS: A bisector cuts a segment or angle into two congruent parts.
Now
Read the following and underline the statements that you understand and circle the statements
that are confusing.
Given: Points X, Y, and Z are collinear. Line AY bisects segment XZ such that a right
angle is formed. Draw a diagram to illustrate this situation. Be sure to label thoroughly.
What I know:
What I wonder:
How can I cope with these moments of confusion?
STOP!
Bisector:
A
perpendicular
bisector of a segment passes through the
Perpendicular
1. Place your compass point on A and stretch
the compass MORE THAN half way to
point B, but not beyond B.
_________________ AND
2. With this length, swing a large arc that will
forms _________________ with the segment.
go BOTH above and below
.
(If you do not wish to make one large
continuous arc, you may simply place one
small arc above
below
Directions
for
constructing
a
Perpendicular Bisector can be found
here
(follow
the
arrows)

and one small arc
.)
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
Using the directions and visual provided in
class, construct a perpendicular bisector of the
segment below.
. Label
the point where the new line and
cross as C.
6.
has now been bisected and AC = CB.
(It could also be said that the segments are
congruent,
.)
Let’s try it again. Using only a compass and a straightedge, construct the perpendicular bisector of
and label it c. [Leave all construction marks.]
Now that you are familiar with the construction of a perpendicular bisector, we must make one last
observation. Using your compass, examine the following pair of segments.
NEW CONSTRUCTIONS:
Inscribed Square: Here are the steps for an Inscribed Square…
How to construct an inscribed square? The construction proceeds as follows:
1. Construct a circle and mark the center point. Make it nice and bold.
2. KEEP THE RADIUS THE SAME.
3. Using a straightedge, draw a diameter.
4. Construct a perpendicular bisector of the diameter. The perpendicular bisector is also a diameter of
the circle.
5. The resulting four points on the circumference of the circle are the vertices of the inscribed square.
6. Connect these four points using a straightedge and there is your square!
Try it below!
SUMMARY:
When I don’t understand a direction a strategy (or strategies) that help me is …