Lesson 1: Moving in the Plane

Let’s describe ways figures can move in the plane.

1.1: Which One Doesn’t Belong: Diagrams

Which one doesn’t belong?   

Four figures labeled A, B, C, and D. each figure is composed of two rays and a point that is located at the endpoints of the two rays.  In figure A the two rays point in opposite directions. In figure B, one ray extends downward and to the right and the other ray extends upward and to the right. the two rays appear to form a right angle. In figure C, one ray extends downward and slightly to the left and the other ray extends downward and slightly to the right. The two rays appear to form an acute angle. In figure D, one ray extends upward and to the left and the other ray extends directly downward. The two rays appear to form an obtuse angle.

1.2: Triangle Square Dance

Your teacher will give you three pictures. Each shows a different set of dance moves.

  1. Arrange the three pictures so one of you can see them right way up. Choose who will start the game.

    • The starting player chooses one of the three applets below and describes the dance to the other player.

    • The other player identifies which dance is being talked about: A, B, or C.

  2. After one round, trade roles. When you have described all three dances, come to an agreement on the words you use to describe the moves in each dance.

  3. With your partner, write a description of the moves in each dance.

Dance A: 

GeoGebra Applet AEJZpFYq

Dance B: 

GeoGebra Applet NSQmZf7q

Dance C: 

GeoGebra Applet edxPr72G

Summary

Here are two ways for changing the position of a figure in a plane without changing its shape or size:

  • Sliding or shifting the figure without turning it. Shifting Figure A to the right and up puts it in the position of Figure B.

A figure that has been slid or shifted in the plane without turning it

  • Turning or rotating the figure around a point. Figure A is rotated around the bottom vertex to create Figure C. 

A figure that has been turned or rotated around a point

Practice Problems ▶