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) _____.
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Constructing Perpendicular Bisectors
During this lesson, we will:
Construct the perpendicular bisector of a segment
Determine properties of perpendicular bisectors
a. AM = MY c. Both a and b.
b. AM + MY = AY d. Neither a nor b.
a. Angle 2 is a right angle.
b. H is the midpoint of BC
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?
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.
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!
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.
If a point lies on the perpendicular bisector of a segment, then it is _______ from each of the endpoints.
Shortest distance measured here!
Absent from class? Click HERE* for step-by-step construction tips.
Please note: This construction example relies upon your first constructing a line segment.
Converse: If a point is equidistant from the endpoints of a segment, then it is on the __________________.
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