Only one plane can pass through three noncollinear points... true or false?

Question

I need help with true and false of geometry.

Please help me find a picture for each to prove them. Or, you can sketch a picture for me, and photograph it so it can be a link...

1. Only one plane can pass through three noncollinear points.

2. If a line intersects a plane that doesn't contain the line, then the intersection is exactly one point.

3. If two lines are perpendicular to the same line, then they're parallel.

~ i believe this is true....

4. If two different planes intersect, then their intersection is a line.

5. If a line and a plane have no points in common, then they are parallel.

6. If a plane intersects two parallel palnes, then the lines of intersection are parallel.

7. If three random planes intersect (no two are parallel and all three do not share the same line), then they divide space into six parts.

THANK YOU!

Answer 1

. Only one plane can pass through three noncollinear points.

True

2. If a line intersects a plane that doesn't contain the line, then the intersection is exactly one point.

True

3. If two lines are perpendicular to the same line, then they're parallel.

False.

This is not always true.  Think of the x, y, and z axes.

4. If two different planes intersect, then their intersection is a line.

True

5. If a line and a plane have no points in common, then they are parallel.

True

6. If a plane intersects two parallel planes, then the lines of intersection are parallel.

True

7. If three random planes intersect (no two are parallel and all three do not share the same line), then they divide space into six parts.

False.

Think of the three planes, xy, xz, and yz.  They divide space into octants (8 parts).

Answer 2

1. True. Picture a triangle. Infinite planes can intersect each leg, but only one plane can intersect the triangle.

2. True. Picture a pin through a piece of paper

3. True. I think this one is self explanatory Edit: assuming they're on the same plane.

4. True. I can't think of a way to describe it, so: http://en.wikipedia.org/wiki/Image:Inter...

5. True. Otherwise they intersect at one point as in 2.

6. True. It's the same as in 3.

7. False. Picture a triangle again, and extend all of the legs into lines. It divides it into seven parts. Edit: The triangle is just from visualizing a fourth plane that the other three intersect.

I hope this helps, I described what I could.

Answer 3

The answers are:

1. T

2. T

3. False (they may be on different planes)

4. T

5. T

6. T

7. Seven