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Math Online

Lesson 10

8.G.1, 8.G.1a, 8.G.1b, 8.G.1c

Properties of Transformations

Two-dimensional figures can be moved on the plane in a variety of

ways. A transformation is an operation that places an original figure,

the preimage, onto a new figure called the image. This process is

called mapping.

Explore a Slide

Arrange ten index cards in a pile.

On the top card, draw a circle at the top right hand corner.

On the next card, draw the same circle slightly down and to the left.

Repeat this for three or four more cards until your circle is at the bottom of the card. Use the remainder of the cards to draw the circle up and to the left.

Place a rubber band around the stack, hold the stack at the rubber band, and flip the cards from front to back.

the Results

1. Describe what you see when you flip the cards from front to back.

2. Which of the following would you use to describe the movement

of the circle on the card: flip, slide, or turn?

Main IdeaIdentify and apply flips, slides, and turns.

New Vocabularytransformationpreimageimagemapping

The original figure is called the preimage.

The figure afterthe movement is called the image.

3. Look at the circles on the first and second cards and then the second and

third cards. How would you describe the change in the position of the circle

from one card to the next?

4. Did the shape or size of the circle change when you moved it? If yes,

explain how the shape or size changed.

Explore a Flip

the Results

5. Use a protractor to find the measure of ∠XYZ and ∠ABC. Did the measure

of the angle change after the flip?

6. Use a centimeter ruler to measure the shortest distance from X and A to the

dotted line. Repeat for Y and B and for Z and C. What do you notice?

7. MAKE A CONJECTURE Write a sentence that would be true for any figure and

its image when the figure is flipped over a line.

and Apply

Copy each figure. Draw the image when each figure is flipped over line �.

8.

�

9.

�

10.

�

Draw right angle XYZ on a piece of tracing paper. Place a line on the paper as shown.

Fold the paper along the line. Trace the angle onto the folded portion of the paper. Unfold and label the angle ABC.

ZY

X

ZY

X

C

A

B

Explore a Turn

the Results

11. Did the shape or size of the trapezoid change when you moved it? If yes,

explain how the shape or size changed.

12. In your first drawing, measure the length of −−

XZ . Did the length of the

segment change after you turned it? Do you think the length would

change after a slide? flip?

13. What is the approximate measure of ∠BAC?

14. MAKE A CONJECTURE In the trapezoid, −−−

WY and −−

XZ are parallel. Were the

segments still parallel after the turn? Would they still be parallel after

a slide? flip?

15. MAKE A CONJECTURE Slides, flips, and turns are called rigid motions of the plane. Based on the activities, describe two characteristics of a rigid

motion of the plane.

Place a second piece of tracing paper over the first. Trace the trapezoid and

��� AB . Place the eraser end of your pencil on A. Turn the second piece

of paper until ��� AB passes through C. Tape the two pieces of paper

together.

B

X

AC

Z

YWWB

X

AC

Z

Y

Copy the trapezoid shown on a piece of tracing paper. Draw points A, B, and C as shown.

Draw ��� AB .

B

X

A C

Z

YW

B

X

A C

Z

YW