Question

Multiple Response: Please select all correct answers and click "submit." Which of the following are among the five basic postulates of Euclidean geometry? Check all that apply. A. A straightedge and compass can be used to create any figure. B. A straight line segment can be drawn between any two points. C. Any straight line segment can be extended indefinitely. D. The angles of a triangle always add up to 180.

Answer 1

To Euclid, a postulate is something that is so obvious it may be accepted without proof.

A. A straightedge and compass can be used to create any figure.

That's not Euclid, that's just goofy.

B. A straight line segment can be drawn between any two points.

That's Euclid's first postulate.

C. Any straight line segment can be extended indefinitely.

That's Euclid's second postulate.

D. The angles of a triangle always add up to 180.

That's true, but a theorem not a postulate. Euclid and the Greeks didn't really use degree angle measurements like we do. They didn't really trust them, I think justifiably. Euclid called 180 degrees "two right angles."

Answer: B C