8.2 - Congruence and Basic Isometries

Introduction:

This is a set of guiding questions and materials for creating your own lesson plan on congruence and basic isometries (translation, rotations, and reflections).

Common Core State Standards:

8.G.1
8.G.2
8.G.3
G-CO.1

Learning Objectives:

What words or concepts come to mind when you think of “geometry”? Make a list.
What does geometry mean?
- Try to elicit a loose etymological definition: geo = earth and metry = measurement.
Why do you think it was given that name?
What uses do you think it had in antiquity?
Is it relevant today?
Do more concepts come to mind now that you are aware of the meaning of geometry?
How do the terms given relate to each other? Do you see any connections?
Can you define any of those terms?
Prompt for circle and square. Take their definitions and construct counterexamples. For instance, if they say that a square is a “shape with four sides,” then draw a rectangle or a clover.
What do we want to avoid in an axiomatic (or any deductive reasoning) system?
Are contradictions and paradoxes acceptable?
- Although they are not, contradictions and paradoxes have been a major force in the development and refinement of mathematics.
Why are right angles 90 degrees?
- Point out that there are several ways to measure angles and that the preferred method in other math courses will be a unit called the radian.

Guiding Questions:

How do the following diagrams compare?

Are any of them the same? In other words, are any of them congruent?
How can you be sure?
How can you get from A to B? A to C? C to B? A to D?

As you elicit responses, introduce/review the basic isometries: translations, rotations, and reflections.

How do you get from left to right?
What isometries do you apply?
Is your solution unique or is there more than one way to get from left to right?

Notes for Teachers:

I have indented some suggestions in the questions above.
We will use the notions introduced here to prove the Pythagorean Theorem in the next lesson.

Video of the Day:

8.2.1 Isometries with Paint

We use the Paint software to illustrate the basic isometries.

8.2.1 Basic Isometries.mp4 Download 8.2.1 Basic Isometries.mp4 Play media comment.