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 a triangle.B.A straight line segment can be drawn between any two points.C.Any straight line segment can be extended indefinitely.D.All circles have 360
Question
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 a triangle.B.A straight line segment can be drawn between any two points.C.Any straight line segment can be extended indefinitely.D.All circles have 360
Solution
The five basic postulates of Euclidean geometry are:
- A straight line segment can be drawn joining any two points.
- Any straight line segment can be extended indefinitely in a straight line.
- Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
- All right angles are congruent.
- 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.
So, from the options you provided:
A. A straightedge and compass can be used to create a triangle. - This is not a postulate of Euclidean geometry.
B. A straight line segment can be drawn between any two points. - This is the first postulate of Euclidean geometry.
C. Any straight line segment can be extended indefinitely. - This is the second postulate of Euclidean geometry.
D. All circles have 360 - This is not a postulate of Euclidean geometry. The postulates do not specify anything about the degrees of a circle.
So, the correct answers are B and C.
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