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9-12 Geometry Unit 1 Lesson 11

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 •Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22

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Lesson 11

11.1 Warm-up 11.2 Activity 11.3 Activity Student Lesson Summary Glossary

Unit 1, Lesson 11

Defining Reflections

Geometry

11.1

Warm-up

What Do You Want to Know?

Triangle has been reflected so that the vertices of its image are labeled points. What is the image of triangle ?

What specific information do you need to be able to solve the problem?

<p>14 points on a circle.</p>

Are You Ready for More?

11.2

Activity

Info Gap: What’s the Point: Reflections

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

Silently read your card and think about what information you need to answer the question.
Ask your partner for the specific information that you need. “Can you tell me ?”
Explain to your partner how you are using the information to solve the problem. “I need to know because . . . .”
Continue to ask questions until you have enough information to solve the problem.
When you have enough information, share the problem card with your partner, and solve the problem independently.
Read the data card, and discuss your reasoning.

If your teacher gives you the data card:

Silently read the information on your card. Wait for your partner to ask for information.
Before telling your partner any information, ask, “Why do you need to know ?”
Listen to your partner’s reasoning and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!
These steps may be repeated.
Once your partner says they have enough information to solve the problem, read the problem card, and solve the problem independently.
Share the data card, and discuss your reasoning.

<p>14 points on a circle.</p>

Are You Ready for More?

11.3

Activity

Does Order Matter?

Here are three congruent L shapes on a grid.

<p>L Shaped Polygons A, B and C on a square grid. A is an upside down L, facing to the right. B is a regular L, facing to the right. C is an L on its side, facing up.</p>

Describe a sequence of transformations that will take Figure A onto Figure B.
If you reverse the order of your sequence, will the reverse sequence still take Figure A onto Figure B?
Describe a sequence of transformations that will take Figure A onto Figure C.
If you reverse the order of your sequence, will the reverse sequence still take Figure A onto Figure C?

Are You Ready for More?

Student Lesson Summary

Think about reflecting the point across line :

<p>Line L, facing downward and to the right. Point A sits to the left of the line.</p>

The image is somewhere on the other side of from . The line is the boundary between all the points (not drawn) that are closer to and all the points that are closer to . In other words, is the set of points that are the same distance from as from . In a previous lesson, we conjectured that a set of points that are the same distance from as from is the perpendicular bisector of the segment . Using a construction technique from a previous lesson, we can construct a line perpendicular to that goes through :

<p>Line L, facing downward and to the right. A perpendicular line passes through Line L and Point A.</p>

lies on this new line at the same distance from as :

<p>Perpendicular lines and a circle</p>

We define the reflection across line as a transformation that takes each point to a point as follows: lies on the line through that is perpendicular to , is on the other side of , and is the same distance from as . If happens to be on line , then and are both at the same location (they are both a distance of zero from line ).

<p>Line l is the perpendicular bisector of AA’.</p>

Glossary

reflection

A reflection is a rigid transformation that is defined by a line. It takes one point to another point that is the same distance from the given line, but on the other side. The segment from the original point to its image is perpendicular to the line of reflection.

In this figure, is reflected across line , and is the image of under the reflection.

Reflect across line .