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

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Presentation transcript:

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

Daily 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 C B A 1 2

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 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.HERE 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 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.

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