Mathematics, 07.07.2019 01:30 nculberson6

Which statement is not one of the axioms of euclidean geometry? a. given any two distinct points, there is exactly one line that contains them. b. every plane contains at least three points that do not lie on the same line. c. if two points lie in a plane, the line containing these points also lies in the plane. d. if two planes intersect, their intersection is a point.

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Answer from: aliceohern

B: Every plane contains at least three points that do not lie on the same line

To answer this question, we will have to state the 5 axioms of Euclidean geometry and they are;

1. A straight line could be drawn between any two points; This means that as long as there is no obstacle between the two points, then we can say that it is possible to draw a straight line between both points. However, if there is an obstacle between the two points, then it is not possible to draw a straight line.

2. Any straight line that is terminated could still be extended indefinitely; A line segment may be bound by an endpoint, but a straight line is not bounded by any endpoint and as a result, it can be extended indefinitely in both directions.

3. A circle could be drawn with any given center point and any given radius; If for example we use a line segment bounded by two end points. If we use one of these 2 endpoints to be the centre of a circle and make the radius of the circle to be equal to the length of the line segment earlier used as an example, it means if we draw a circle, it will have a diameter that is twice the length of that same line segment.

4. All right angles are definitely equal; A right angle always has a measurement of 90°. This means that regardless of its' orientation, it will still remain 90°.

5. For any given point that is not on a given line, there will be exactly one line passing through the point that would not meet that same given line; This implies that two lines will be parallel to each other if they intersect a third line with the interior angle between them being 180°.

Looking at the given options in the question, the only one that doesn't correspond to any of these 5 axioms I have stated would be option B.

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Which statement is not one of the axioms of euclidean geometry? a. given any two distinct points,...

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