Which of the following is not a postulate of Euclidean geometry?A.All right angles can be bisected.B.Through a given point not on a given line, there is exactly one line parallel to the given line.C.A straight line segment can be drawn between any two points.D.Any straight line segment can be extended indefinitely.
Question
Which of the following is not a postulate of Euclidean geometry?A.All right angles can be bisected.B.Through a given point not on a given line, there is exactly one line parallel to the given line.C.A straight line segment can be drawn between any two points.D.Any straight line segment can be extended indefinitely.
Solution
The statement "All right angles can be bisected" is not a postulate of Euclidean geometry. The other three statements are indeed postulates of Euclidean geometry.
Here's why:
A. All right angles can be bisected - This is not a postulate of Euclidean geometry. While it is true that all right angles can be bisected, this is a consequence of the postulates, not a postulate itself.
B. Through a given point not on a given line, there is exactly one line parallel to the given line - This is Euclid's fifth postulate, also known as the parallel postulate.
C. A straight line segment can be drawn between any two points - This is Euclid's first postulate.
D. Any straight line segment can be extended indefinitely - This is Euclid's second postulate.
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