Lesson 12

Part II (Geometry and Animation, continued)

In this part, we will use the animation table to explore what is happening to measurements during an animation.

1. Drawing a Circle's Diameter

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2. Minor Exploration

3. Viewing a Measurement with the Animation Table

During the first half of the sixth century B.C., a gentleman named Thales discovered that an angle inscribed in a semicircle will always be a right angle. This discovery is today referred to as Thales’ Theorem:

Thales' Theorem
An angle inscribed in a semicircle is a right angle.

So, if you ever need to construct a right triangle just draw a triangle in a semi-circle (half circle) and use the diameter as the hypotenuse.

Other results Thales is credited for:

4. Getting Ready to Analyze Area

5. Changing the Diameter to be Horizontal

6. Setting up an Animation to Generate Areas to Analyze

7. Displaying the Triangle's Area in the Window

8. Analyzing Area and Animation

9. Viewing the x-Value and Area Graphically

Part II


Practice Exercises

  1. Open the eActivity named L12_PartII_a (in the Lesson 12 folder).
  2. Expand the Geometry strip.
  3. Select point B and line segment DE.
  4. Add an animation to animate point B along line segment DE.
  5. Run your animation.
  6. Get a screen capture and paste it into your Lesson12 document (under a title of PART II).
  7. Advance the toolbar, deselect everything and then select points A, B and C. The area of triangle ABC should be showing in the measurement box.
  8. Create an animation table showing the areas. Scroll the table to show the largest area.
  9. Get a screen capture. Add two blank spaces following the first screen capture and then paste this one.
  10. Save your work as an eActivity named L12_PartII_a_your initials here.
  11. Open the eActivity named L12_PartII_b.
  12. Add an animation to animate point B along line segment DE.
  13. Run your animation.
  14. Create an animation table showing the areas of the triangle during animation.
  15. Why do you think the areas in this animation are the same? Inside the eActivity window type: The areas are the same because… Be sure to complete the sentence.
  16. Get a screen capture. Add two blank spaces following the second screen capture and then paste this one.
  17. Save your work as an eActivity named L12_PartII_b_your initials here.