Explain the difference between area, volume, and surface area.

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1. Explain the difference between area, volume, and surface area. Select a geometric shape and give an example of how to calculate its surface area and volume. How would you teach these concepts to a class?

2. Describe each of the trigonometric ratios in terms of the sides of a right triangle. Why can we be sure that sin 30° always has the same value regardless of the size of the right triangle containing the 30° angle?
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3. Define similar triangles and similar figures. Compare and contrast the various theorems which relate to the similarity of triangles. How would you teach these theorems to a class? Give examples.

4. What is a tessellation, how are tessellations used, and what must happen at vertices in order for polygons to tessellate?

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