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9-12 Integrated Math 1 Unit 1 Lesson 3

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Lesson 3

3.1 Warm-up 3.2 Activity 3.3 Activity Student Lesson Summary Glossary

Unit 1, Lesson 3

Construction Techniques 1: Perpendicular Bisectors

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Integrated Math 1

3.1

Warm-up

Find All the Points!

Here are 2 points labeled and , and a line segment :

<p>Two points, A and B, and a vertical line segment with endpoints C and D.</p>

Mark 5 points that are a distance away from point . How could you describe all points that are a distance away from point ?
Mark 5 points that are a distance away from point . How could you describe all points that are a distance away from point ?
In a different color, mark all the points that are a distance away from both and at the same time.

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3.2

Activity

Human Perpendicular Bisector

Your teacher will mark points and on the floor. Decide where to stand so you are the same distance from point as you are from point . Think of another place you could stand in case someone has already taken that spot.

After everyone sits down, draw a diagram of what happened.

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3.3

Activity

How Well Can You Slice It?

Use the tools available to find the perpendicular bisector of segment .

After coming up with a method, make a copy of segment on tracing paper and look for another method to find its perpendicular bisector.

<p>Line segment with endpoints P and Q.</p>

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Student Lesson Summary

A perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to it. Recall that a right angle is the angle made when we divide a straight angle into two congruent angles. Lines that intersect at right angles are called perpendicular.

A conjecture is a guess that hasn't been proven yet. We made a conjecture that the perpendicular bisector of segment is the set of all points that are the same distance from as they are from . This turns out to be true. The perpendicular bisector of any segment can be constructed by finding points that are the same distance from the endpoints of the segment. Intersecting circles with the same radius centered at each endpoint of the segment can be used to find points that are the same distance from each endpoint, as circles show all the points that are a given distance from their center point.

<p>Two congruent circles, each pass through the center of the other at A and B, radius AB is drawn. A vertical line through both circles’ intersection points, labeled point C at the top intersection.</p>

Glossary

conjecture

A conjecture is a reasonable guess that someone is trying to either prove or disprove.

perpendicular bisector

The perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to the segment.

In this diagram, the dashed line is the perpendicular bisector of segment .

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