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GeoGebraGeoGebra Classroom

Better Wump Hats

Clearly the Wumps need better hats, but they need to be able to scale like the Wumps do. Design a better hat below, and see what it looks like at different scales. You can move the original blue hat by clicking in the hat and dragging. To move the green image hat, click and drag A'.

1) How do the angles in the enlarged hat compare to your design? How can you tell?

2) Set the scale slider to 2. How do the side lengths in the image compare to the original? Find the lengths of 3 pairs of corresponding sides.

3) Set the scale slider to NOT be a whole number. (Like 1.5, 2.5, 3.5 ...) How do the side lengths in the image compare to the original? Find the lengths of 3 pairs of corresponding sides.

4) These two hats are similar, but how could you prove it to someone?

5) What is the scale of this enlargement? How do you know?

6) Design a new hat. If you select the length tool and click on a polygon, it will tell you the perimeter. Find the perimeter for three different scales and enter them in the table. Compare perimeters of the images to the perimeter of the original hat (scale=1). How does scale effect perimeter? How do you know?

7) If you select the area tool and click on a polygon, it will tell you the area. Find the area for three different scales and enter them in the table. Compare areas of the images to the area of the original hat (scale=1). How does scale effect area? How do you know?

EXTENSIONS

What if we had a 3D object?

X1) We're working with two dimensional similarity. What if we enlarged a three dimensional hat? How could you tell if two three dimensional objects were similar?

X2) How do you think the scale of an enlargement would affect the volume of a 3D similar object? Why do you think?

Use the applet below to experiment with 3D similarity. You can change the original prism by moving A. (Click once to move side to side; click again to move up and down.) You can also turn the image to see the similar prisms in 3D.

X3) What did you notice or wonder while playing with the 3D similar objects?