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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. What did the Pythagorean Theorem accomplish for mathematics?**
**(a)** The concept of providing a logical proof. **(b)** The concept of constructing useful mathematics. **(c)** The ability to measure angles. **(d)** The ability to find square roots.

**2. What did Dunham consider extraordinary about the Elements?**
**(a)** The content was totally unique. **(b)** How Hippocrates ordered the book. **(c)** The content was not based on previous authors' work. **(d)** How geometric proofs were presented.

**3. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?**
**(a)** Circle. **(b)** Intersection. **(c)** 180 degree angle. **(d)** Parallel lines.

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

**5. What does the Pythagorean Theorem state?**
**(a)** For any right triangle the diagonal side is equal to the sum of the legs. **(b)** For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs. **(c)** For any triangle the sqaured sum of the legs is equal to half the hypotenuse. **(d)** For any triangle the sum of the legs squared is equal to the length of the hypotenuse.

## Short Answer Questions

**1.** In Elements, how many postulates must be accepted as given?

**2.** Which of Euclid's postulates troubled many of the following generations of mathematicians?

**3.** Who was the first of ancient philosophers to consider why geometric properties existed?

**4.** What was most useful about finding the square of a shape, before Hippocrates?

**5.** After Hippocrates, what shape did the Greeks attempt to square without success?

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