1. Constructing Perpendicular Bisectors
During this lesson, we will:
Construct the perpendicular bisector of a segment
Determine properties of perpendicular bisectors

2. Daily Warm-Up Quiz
A point which divides a segment into two congruent segments is a(n) _____.
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.
Mark the figure based upon the given information:
a. Angle 2 is a right angle.
b. H is the midpoint of BC H C B A

3. I wonder how many segment bisectors I can draw through the midpoint?
Before we start:
a line, segment, or ray which intersects a segment at its midpoint
Segment Bisector: ________________ ______________________________
I wonder how many segment bisectors I can draw through the midpoint?

4. 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.

5. Definition: 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!

6. Investigation 1: Perpendicular Bisector Conjecture
STEP 1 Pick three points X, Y, and Z on the perpendicular bisector.
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. Z Y X

7. Investigative Results: Perpendicular Bisector Conjecture
If a point lies on the perpendicular bisector of a segment, then it is _______ from each of the endpoints.
Converse: If a point is equidistant from the endpoints of a segment, then it is on the __________________.
perpendicular bisector
equidistant
Shortest distance measured here!

8. 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.

9. Final Checks for Understanding
Construct the “average” of HI and UP below.
_______________ _______
H I U P
2. Name two fringe benefits of constructing perpendicular bisectors of a segment.
3.* By construction, divide a segment into fourths (four congruent segments).
4. BONUS: Construct a segment which is ¾ the length of your original segment in #3 above.

10. 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