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A square has been constructed in purple. The light blue square is its rotation, which is controlled by the slider on the top. Your goal is to get the purple and light blue squares to completely overlap, so that it looks like there is only one dark blue shape.
Start by dragging the point on the slider to 0. Notice the squares overlap. Now slowly drag the point to the right till the shape overlaps again. Drag the point all the way to the right. Each time the squares overlap, record the measure of the angle on the slider. (Remember, its hard to get perfect overlaps so I'll tell you the angles you're looking for all even whole numbers.)
1. How many times did the purple and blue squares overlap? Do not count the starting position, but DO count the end position.
2. List the angle measurements where the shapes overlapped. You should have the same number of angle measurements as your answer to question 1. Also, they should all be multiples of the first angle measure!