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Geometry 10-4a GeoGebra Primer: Perimeter & Area of Similar Figures Exploration

By Matthew Richardson
Last updated over 3 years ago
5 questions
Explore the GeoGebra applet below before completing the items that follow.

Exploration: What impact does dragging point D have on the diagram?

Exploration: What impact does dragging the slider have on the diagram?

Exploration: The slider changes the value of k. What does k represent?

Exploration: Categorize each statement as always, sometimes, or never true.

  • The areas of the triangles are equivalent.
  • The blue triangle is an image of the red triangle after a dilation with scale factor >1.
  • Dragging the slider to the right increases the side lengths of the blue triangle.
  • The two triangles are similar.
  • Dragging the slider to the left increases the area of the blue triangle.
  • Dragging the slider to the right decreases the area of the red triangle.
  • Always
  • Sometimes
  • Never
The same applet from above is embedded again below for convenience as you continue the activity.

Exploration: Set k to an arbitrary value with k ≠ 1. Copy the sentences below, paste them into the response field, and replace the blanks with information that matches the configuration you've set in the applet. You may use the embedded Desmos calculator below.

With scale factor k set to __?__, each side length in the image is exactly __?__ times as large as its corresponding side length in the preimage. A direct result is that the perimeter of the image is also exactly __?__ times as large as the perimeter of the preimage. The area of the image, on the other hand, is exactly __?__ times as large as the area of the preimage.