Which of the following are among the five basic postulates of Euclidean geometry?Check all that apply.A.All circles have 360.B.A straight line segment can be drawn between any two points.C.A straightedge and compass can be used to create a triangle.D.Any straight line segment can be extended indefinitely.SUBMITarrow_backPREVIOUS
Question
Which of the following are among the five basic postulates of Euclidean geometry?Check all that apply.A.All circles have 360.B.A straight line segment can be drawn between any two points.C.A straightedge and compass can be used to create a triangle.D.Any straight line segment can be extended indefinitely.SUBMITarrow_backPREVIOUS
Solution
The correct postulates according to Euclidean geometry from the options provided are:
B. A straight line segment can be drawn between any two points. This is the first postulate of Euclidean geometry which states that a straight line segment can be drawn joining any two points.
D. Any straight line segment can be extended indefinitely. This is the second postulate of Euclidean geometry which states that any straight line segment can be extended indefinitely in a straight line.
Option A is incorrect because it is not a postulate of Euclidean geometry. The statement about all circles having 360 degrees is a fact about the measure of the total degrees in a circle, not a basic assumption of Euclidean geometry.
Option C is also incorrect. While it's true that a straightedge and compass can be used to create a triangle, this is not one of the five basic postulates of Euclidean geometry.
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