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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. Which of the following is an example of a postulate that must be accepted in Elements?**
**(a)** It is possible to draw a straight line between an infinite number of points. **(b)** It is possible to draw a circle that contains no lines. **(c)** It is possible to connect any two points with a line and make a circle. **(d)** It is possible to draw an arc with any three points.

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

**3. In Elements, how many postulates must be accepted as given?**
**(a)** Twenty-two. **(b)** Eighteen. **(c)** Twelve, **(d)** Five.

**4. What did Euclid do in his 48th proposition?**
**(a)** Euclid proved the converse of the Pythagorean Theorem. **(b)** Euclid demonstrated how to use the Pythagorean Theorem. **(c)** Euclid demonstrated the faults of the Pythagorean Theorem. **(d)** Euclid proved the Pythagorean Theorem.

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

## Short Answer Questions

**1.** What instruments did the Greeks use to square a shape?

**2.** Which words best describe how solid proofs were developed in Elements?

**3.** What did Ferdinand Lindeman prove in 1882?

**4.** What did Hippocrates do that advanced mathematical methods?

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

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