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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 was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?**
**(a)** Euclid constructed squares on the sides of right triangles. **(b)** Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs. **(c)** Euclid used propositions about similar angles and parallel lines. **(d)** Euclid used his own axioms and propositions to show relationships,

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

**3. 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 an arc with any three points. **(c)** It is possible to draw a circle that contains no lines. **(d)** It is possible to connect any two points with a line and make a circle.

**4. How many definitions were stated in Elements?**
**(a)** Thirty. **(b)** Five. **(c)** Twenty-three. **(d)** Eighteen.

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

## Short Answer Questions

**1.** Which is one of the common notions presented in Elements?

**2.** Which of the following was NOT one of Gauss' discoveries?

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

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

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

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