Constructing perpendicular bisectors
This presentation is the property of its rightful owner.
Sponsored Links
1 / 11

Constructing Perpendicular Bisectors PowerPoint PPT Presentation


  • 65 Views
  • Uploaded on
  • Presentation posted in: General

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) _____.

Download Presentation

Constructing Perpendicular Bisectors

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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

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


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 perpendicular bisector

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

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

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


Investigative results perpendicular bisector conjecture

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

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 segment1

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

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.


Enrichment

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


  • Login