Question

Which statement is NOT one of the axioms of Euclidean geometry?

Answer 1

1.Given any two distinct points, there is exactly one line that contains them.
2.Every plane contains at least three points that do not lie on the same line.
3.If two points lie in a plane, the line containing these points also lies in the plane.
4.If two planes intersect, their intersection is a point.

Answer 2

Refer to http://mathworld.wolfram.com/EuclidsPostulates.html

Answer 3

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 4

Oops, looks like it's talking about 3D geometry so these 5 axioms are not useful

Answer 5

Well, if you think about the four options, one of them is actually not true

Answer 6

i know im just having trouble figureing out which one,

Answer 7

"Given any two distinct points, there is exactly one line that contains them."
Is this true?

Answer 8

wait no because the intersect something like that and i think it's opposite

Answer 9

@T-dog2660

Did you consider this:

.If two planes intersect, their intersection is a point.

Answer 10

I'm not saying that it is the correct answer. I'm wondering if you see anything odd about it?

Answer 11

@T-dog2660

Go here and read the sixth postulate.
http://www.cliffsnotes.com/math/geometry/fundamental-ideas/postulates-and-theorems

Return and choose the answer to the question.

Answer 12

would it be 2?

Answer 13

>>>> would it be 2? No

What does the sixth postulate at the link above say?

Post it here, okay? All of us will look at it and help you decide.

Answer 14

Postulate 6: If two planes intersect, then their intersection is a line.

Answer 15

oh wait so 4 is the answer then?

Answer 16

Correct.

Answer 17

thanks for the help directrix!

Answer 18

You are welcome.