Constructing Constructing Perpendicular BisectorsPerpendicular Bisectors

During this lesson, we will:Construct the perpendicular bisector of a segmentDetermine properties of perpendicular bisectors

Daily Warm-Up QuizDaily 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

information: a. Angle 2 is a right angle.

b. H is the midpoint of BC

H CB

A

1 2

Before we start: 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 Paper-Folding a Perpendicular BisectorPerpendicular 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 STEP 1 Pick three points X, Y, and Z on the perpendicular bisector.

STEP 2 STEP 2 From each point, draw segments to each of the endpoints. STEP 3 STEP 3 Use your compass to compare the following segment: a.) AX and BX, b.) AY and BY, and c.) AZ & BZ.

X

Y

Z

Investigative Results: 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 UnderstandingFinal 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.

ENRICHMENTENRICHMENT

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 sideMidsegment: Segment which connects the midpoints of two sides of a triangle