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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 is one of the common notions presented in Elements?**
**(a)** "Things with are equal have an inverse that is equal." **(b)** "The inverse of a line makes a circle." **(c)** "Things which are equal to the same thing are also equal to each other." **(d)** "Points with equal values can be connected with a line of equal value."

**2. What instruments did the Greeks use to square a shape?**
**(a)** A sphere and ruler. **(b)** A compass and a ruled straight-edge. **(c)** A pendulum. **(d)** A small grid.

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

**4. How did Lindeman prove his conclusion?**
**(a)** Lindeman proved that all numbers are constructable with a compass and ruler. **(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 some numbers are not constructable with only a compass and straight-edge.

**5. Which of the following becomes an important definition in mathematics that was first presented in Elements?**
**(a)** Parallel line. **(b)** Circle. **(c)** 180 degree angle. **(d)** Intersection.

## Short Answer Questions

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

**2.** What was the bases of Hippocrates's proof ?

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

**4.** What was true about Hippocrates's proof?

**5.** What did Euclid do in his 48th proposition?

This section contains 411 words(approx. 2 pages at 300 words per page) |