Question

Which of the following were among the five basic postulates of Euclidean geometry? Check all that apply.
A. Through a point not on a given line, there is exactly one line parallel to the given line.
B. There is a straight line segment between any two points.
C. All right angles are equal to each other.
D. A circle can be drawn with any center and radius.

Answer 1

1. A straight line segment can be drawn joining any two points.

2. Any straight line segment can be extended indefinitely in a straight line.

3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.

4. All right angles are congruent.

5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate.

Answer 2

Thank you

Answer 3

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