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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