True or False?

The following exercises will help you visualize relationships between geometric figures in a plane and in space. Determine whether the following statements are true or false. Make a sketch or use physical objects to demonstrate each true statement. For each false statement, produce a counterexample illustrating that each is false. If you wish to create physical models, use pencil tips and thumbtacks to represent points. Use rulers, pencils, or stiff wires to represent lines. Use a piece of paper or cardboard to represent planes. Some of these can be challenging I know which is why I am asking you to make a PHYSICAL model to help you visualize the statement.

1. For every line segment, there is exactly one midpoint.
2. For every angle, there is exactly one angle bisector.
3. If two different lines intersect, then they intersect at one and only one point.
4. If 2 different circles intersect, then they intersect at one and only one point.
5. There is exactly one and only one line perpendicular to a given line through a given point on the given line.
6. In a plane, there is exactly one line perpendicular to a given line through a given point on the given line.
7. There is exactly one line perpendicular to a given line through a given point NOT on the given line.
8. In every triangle, there is exactly one right angle.
9. Through a given point NOT on a given line, there is one and only one line that can be constructed parallel to the given line.
10. It is possible for 2 triangles to intersect in one point, 2 points, 3 points, 4 points, 5 points, or 6 points, but not exactly 7 points.
11. One and only one distinct line can be drawn through 2 different points.
12. One and only one distinct plane can be made to pass through 3 NONcollinear points.
13. Exactly one disitinct plane passes through one line and a point NOT on the line.
14. If a line intersects a plane NOT containing it, then the intersection is exactly one point.
15. If 2 lines are perpendicular to the SAME line, then they are parallel.
16. If 2 different planes intersect, then their intersection is a line.
17. If a line and a plane have NO points in common, then they are parallel.
18. If 2 coplanar lines are BOTH PERPENDICULAR to a third line in the SAME plane, then the 2 lines are parallel.
19. If 2 different planes do NOT intersect, then they are parallel.
20. If a plane intersects 2 parallel planes, then the LINES OF INTERSECTION are parallel.
21. If 3 RANDOM planes intersect (no 2 planes are parallel and no 3 through the same line), then they divide space into 6 parts.
22. If a line is perpendicular to 2 lines in a plane, but the lines is NOT contained in the plane, then the line is perpendicular to the plane.
23. If 2 lines are perpendicular to the same plane, then they are parallel to each other.