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IM Geo.1.14 Lesson: Defining Rotations

Autor:GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

For each figure, which pair of angles appears congruent? How could you check?



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 data card:If your teacher gives you the problem card:
  1. Silently read the information on your card.
  2. Ask your partner “What specific information do you need?” and wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)
  3. Before telling your partner the information, ask “Why do you need to know (that piece of information)?”
  4. Read the problem card, and solve the problem independently.
  5. Share the data card, and discuss your reasoning.

  1. Silently read your card and think about what information you need to answer the question.
  2. Ask your partner for the specific information that you need.
  3. Explain to your partner how you are using the information to solve the problem.
  4. When you have enough information, share the problem card with your partner, and solve the problem independently.
  5. Read the data card, and discuss your reasoning.

Do not show or read your card to your partner.

Use the applet below:

Draw a segment. Label the endpoints  and .

  • Rotate segment  clockwise around center  by 90 degrees. Label the new endpoint .
  • Use the Polygon tool to draw triangle .
What kind of triangle did you draw?

What other properties do you notice in the figure? Explain your reasoning.

Use the applet below:

Draw a segment. Label the endpoints  and .

  • Rotate segment  counterclockwise around center  by 30 degrees. Label the new endpoint.
  • Rotate segment  counterclockwise around center  by 30 degrees. Label the new endpoint .
  • Use the Polygon tool to draw triangle .
What kind of triangle did you draw?

What other properties do you notice in the figure? Explain your reasoning.

You constructed an equilateral triangle by rotating a given segment around one of its endpoints by a specific angle measure.

An equilateral triangle is an example of a regular polygon: a polygon with all sides congruent and all interior angles congruent. Try to construct some other regular polygons with this method.

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