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Constructing Perpendicular Bisectors

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

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

  2. 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

  3. 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?

  4. 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.

  5. 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!

  6. 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

  7. Investigative Results: Perpendicular Bisector Conjecture Converse: If a point is equidistant from the endpoints of a segment, then it is on the __________________. If a point lies on the perpendicular bisector of a segment, then it is _______ from each of the endpoints. equidistant perpendicular bisector Shortest distance measured here!

  8. 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.

  9. 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. 3.* By construction, divide a segment into fourths (four congruent segments). 4. BONUS: Construct a segment which is ¾ the length of your original segment in #3 above.

  10. 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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