Rotations

Triangles

• To discover rotations we first need to make a center.

  • Draw a point and select it. Then under Transform, select MARK CENTER.

  Draw a point

• Draw a triangle. Select your triangle (vertices, sides, and interior). Then choose ROTATE under the TRANSFORM menu. Enter 120.

Rotation of the Triangle

• Move the vertices and notice what happens.

Moving Point B
Moving Point C
Moving Point D

• Now lets move Triangle BCD around and notice what occurs.

Moving the original triangle

• Move the center point around as well.

Moving the center point

• Let us join the points of our original reflection to the corresponding points using the segment tool. What do you notice?

Joining corresponding points

 

• Move the center point inside of the original triangle. What do you notice?

Moving the point inside the original

• Now reshape te triangle so that it exactly fits on top of itself.

Reshaping Triangle

Quadrilaterals

• Does this work with quadrilaterals? Lets find out!
  • KEEP YOUR CENTER POINT!
  • Draw a quadrilateral.
  • Select the quadrilateral (sides, points, and interior).
  • Go to TRANSFORM and then select ROTATE.
  • Enter 180 degrees.

Rotation of quadrilateral

• Move the images around like we did with the triangles.
• NOW, let us connect the corresponding vertices. What do you notice?

Connecting the vertices

You should notice the symmetry that occurs by connecting the corresponding points. This did not happen when we connected the vertices of the triangle. If you were to measure the angles you will notice same angle measurements of the corresponding angles.

More fun with rotations!

• Now let us start a new sketch and let us draw an angle.
  • Draw two segments with a common endpoint.

  Construction of the angle

• Now construct a triangle.
• Highlight the three points that make up the angle.
  • Under the TRANSFORM menu, select ROTATE.
  • Now select BY MARKED ANGLE.
  • What do you notice?

  Adjusting the angle

• Play with the angles and see how the images change.

Changing the angle measurement

The angle that you drew changes the amount of images are rotated. As the degree of the angle gets closer to 0 degrees, the rotated image and the original image become closer.

Reflections

Translations

Write Up 3