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This quiz consists of 5 multiple choice and 5 short answer questions through Euclid's Proof of the Pythagorean Theorem.

## Multiple Choice Questions

**1. How do we know about Hippocrates proofs and theorems?**
**(a)** What we know is from references of later mathematicians. **(b)** What is known from archived documents of his time. **(c)** His books and publications. **(d)** Mathematicians rewrote all of his proofs after his death,

**2. According to Euclid, when is a triangle a right triangle?**
**(a)** When a triangle has three sides whose squares are equal to the area of the triangle. **(b)** When a triangle can be constructed with three unequal sides. **(c)** When a triangle has a side whose square is the sum of the squares of the two legs. **(d)** When a triangle does not have a side which can be considered a hypotenuse.

**3. What were the proofs in Elements based on?**
**(a)** Basic definitions. **(b)** Novel notions. **(c)** Ancient greek geometry. **(d)** Lindeman's method.

**4. What did Hippocrates do that advanced mathematical methods?**
**(a)** He created a new ways to disprove theories. **(b)** He proved that mathematics can be applied in a unlogical order. **(c)** He demonstrated that geometry does not have to be based on previous knowledge. **(d)** He built theorems based on sequencially more complex proofs.

**5. How did Lindeman prove his conclusion?**
**(a)** Lindeman proved that square roots are irrational numbers. **(b)** Lindeman proved that some numbers are not constructable with only a compass and straight-edge. **(c)** Lindeman proved that all numbers are constructable with a compass and ruler. **(d)** Lindeman proved that some numbers are constructable without the use of a compass.

## Short Answer Questions

**1.** What did Dunham consider extraordinary about the Elements?

**2.** What is the name for determining the area of an enclosed space by constructing a square of equivalent area?

**3.** "Straight lines in the same plane that will never meet if extended forever" is a definition of what?

**4.** Which of the following is an example of a postulate that must be accepted in Elements?

**5.** Which of the following becomes an important definition in mathematics that was first presented in Elements?

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