Geometry (2)

23.) Two planes can intersect in a single point.
This is wrong because two planes always either do not intersect (i.e. parallel plane) or the intersection is a line, but never a point.

To think about this, take two pieces of papers.
You can lift one above the another, this is the parallel plane case, they will never intersect.

You can also fold one piece of paper along any line, and imagine the two sides as different planes, this is the intersect in a line case.

Just fiddle with the paper, you can never make it intersect at a point.

24.) Three point have to be collinear.

This is wrong because the three points on a triangle is not collinear. (Remember collinear means they are ALL on the same line, which is obviously wrong for three points on a triangle)

25.) A line is contained in exactly one plane.

Looking back at problem 23. We said when two planes intersect, the intersection is a line, right. That line is contains in both planes, that is why a line is contained in exactly one plane is wrong.

26.) If $ x^2 = 25 $, then $ x = 5 $

This is also wrong, as it is possible for $ x = -5 $