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Constructing Perpendicular BisectorsPowerPoint Presentation

Constructing Perpendicular Bisectors

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### Constructing Perpendicular Bisectors

During this lesson, we will:

Construct the perpendicular bisector of a segment

Determine properties of perpendicular bisectors

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

A

B

1 2

C

H

Before we start:

Segment Bisector: ______________________________________________

a line, segment, or ray 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.

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

Investigative Results: Perpendicular Bisector Conjecture

If a point lies on the perpendicular bisector of a segment, then it is _______ from each of the endpoints.

equidistant

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

- 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

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