Transcript Constructing Perpendicular Bisectors

Constructing Perpendicular
Bisectors
During this lesson, we will:
 Construct the perpendicular bisector of a
segment
 Determine properties of perpendicular
bisectors
Daily Warm-Up Quiz
1. A point which divides a segment into
two congruent segments is a(n) _____.
2. If M is the midpoint of AY, then
a. AM = MY
c. Both a and b.
b. AM + MY = AY d. Neither a nor b.
3. Mark the figure based upon the given
A
information:
a. Angle 2 is a right angle.
b. H is the midpoint of BC B
1
H
2
C
Before we start:
a line, segment, or ray
Segment Bisector: ________________
which
intersects a segment at its midpoint
______________________________
I wonder how
many segment
bisectors I
can draw
through the
midpoint?
Paper-Folding a Perpendicular
Bisector
STEP 1 Draw a segment on patty paper.
Label it OE.
STEP 2 Fold your patty paper so that the
endpoints O and E overlap with one another.
Draw a line along the fold.
STEP 3 Name the point of intersection N.
Next, measure a. the four angles which are
formed, and b. segments ON and NE.
Definition: Perpendicular
Bisector
Perpendicular bisector: _____________
a line, ray, or
_______________________________
segment that a. intersects a segment at
_______________________________
its midpoint and b. forms right angles (90)
Add each
definition to
your
illustrated
glossary!
Investigation 1: Perpendicular
Bisector Conjecture
STEP 1 Pick three points X, Y, and Z on the
perpendicular bisector.
Z
Y
X
STEP 2 From each point, draw segments to each of the
endpoints.
STEP 3 Use your compass to compare the following
segment: a.) AX and BX, b.) AY and BY, and c.) AZ & BZ.
Investigative Results: Perpendicular
Bisector Conjecture
If a point lies on the perpendicular
equidistant
bisector of a segment, then it is _______
from each of the endpoints.
Shortest distance
measured here!
Construction: Perpendicular
Bisector, Given a Line Segment
Absent from class?
Click HERE* for
step-by-step
construction tips.
Please note: This construction example relies upon
your first constructing a line segment.
Construction: Perpendicular
Bisector, Given a Line Segment
Converse: If a point is equidistant from the
endpoints of a segment, then it is on the
perpendicular
bisector
__________________.
Final Checks for Understanding
1. Construct the “average” of HI and UP
below.
_______________ _______
H
I U
P
2. Name two fringe benefits of constructing
perpendicular bisectors of a segment.
ENRICHMENT
Now that you can construct perpendicular
bisectors and the midpoint, you can
construct rectangles, squares, and right
triangle. Try constructing the following,
based upon their definitions.
Median: Segment in a triangle which
connects a vertex to the midpoint of the
opposite side
Midsegment: Segment which connects the
midpoints of two sides of a triangle