1. A point is:
a. the idea of location or place.
b. the foundational geometric object.
c. the object from which all other geometric objects are defined.
2. Distance is the idea of proximity.
2. Path describes the distance between any two points.
3. Between any two points, there are infinitely many paths.
4. The measure of distance is called length.
5. The path with the least length between any two points is called a straight line.
6. Area is the idea of surface.
7. A plane is a flat area.
8. Given any magnitudes, an average is that value each of the magnitudes would
have if they were equal or made to be equal.
9. Straight lines in a plane which never meet even if extended indefinitely at either end,
are called parallel lines.
10. A geometric object whose opposite sides are equal and parallel is called a parallelogram.
11. For any parallelogram, the average length of the lengths of infinite parallel lines it contains, is
equal to one of its sides.
12. A triangle is a geometric object described by the shortest paths joining three points in a plane.
13. The point at which two planar lines meet or intersect in a plane is called a vertex or corner.
14. An angle is the idea of orientation or inclination between two intersecting planar lines from
their vertex in the plane.
15. If two planar lines cross each other in a plane forming four equal angles, then each of these
angles is called a right angle.
16. Any triangle that contains one right angle is called a right angled triangle.
17. The side of greatest length in a right angled triangle, is called a hypotenuse.
18. A diagonal is a line that cuts a parallelogram in two identical triangles.
19. Any parallelogram whose sides all meet at right angles is called a rectangle.
20. The diagonal of a rectangle is the hypotenuse of the two right angled triangles.
21. The shortest length between the diagonal end points of a rectangle is the diagonal.
22. Comparison of parallelogram areas is called rectangular area measure.
23. For any right-angled triangle it can easily be proved that the square on the hypotenuse is
equal to the sum of the squares formed on the remaining two sides of the same triangle.
24. The shortest length between any two points in a plane can be indirectly described by the
square of the hypotenuse length, if these points are the endpoints of the hypotenuse.