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

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

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

**4. Who was the first of ancient philosophers to consider why geometric properties existed?**
**(a)** Aristotle. **(b)** Thales. **(c)** Pythagoras. **(d)** Hippocrates.

**5. What was the bases of Hippocrates's proof ?**
**(a)** Properties of points and lines. **(b)** Properties of squares and cubes. **(c)** Properties of triangles and semicircles. **(d)** Properties of area to volume measurements.

## Short Answer Questions

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

**2.** Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

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

**4.** What provided most of the content in the book Elements?

**5.** What was Hippocrates's great advance to mathematics?

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