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2 is a prime number. It is the only even prime.

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1 is not a prime. This is a convention. The number 1 fits the definition of prime we have given, since it is only divisible by itself -- one -- and one. However, an important theorem in mathematics, called the fundamental theorem of arithmetic, says that every integer greater than one is either prime or can be expressed as a unique product of prime numbers. If 1 is considered a prime, this would no longer be the case. Consider: 10 = 2 x 5. But 10 = 1 x 2 x 5. But 10 = 1 x1 x 1 x 1 x 1 x 2 x 5.

The fundamental theorem of arithmetic is essential for proving many mathematical results, so it would never do to allow 1 to be a prime!

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Two inputs to a function may give the same output. In this case, many numbers produce the output "yes," and many will produce the output "no."

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Not every function can be undone. In this case, if the output is "yes," for example, there's no way of knowing what the input was. (You may want to discuss how this is related to the point above.)

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No matter what shape triangle you start with, you end up with four identical triangles inside your original triangle. Three are oriented the same way as the original triangle, and one is upside down.

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The four triangles are all similar to the original. For example, if you connect the midpoints of a right triangle, you will end up with right triangles inside.

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The areas of each of the triangles are 1/4 the area of the original (since there are 4 of them, and they are identical).

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The inside figure of the quadrilateral is a parallelogram. That is, opposite sides are parallel. It doesn't necessarily resemble the outer figure at all.

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The inside figure of a quadrilateral contains half the original area (this may be more difficult to see).