Geometry Basics

Question

Choose five terms, some from geometry and some from other areas of mathematics, and give a precise definition of each.

Then change each of those definitions so that it still describes the term but not precisely enough to avoid ambiguity. Write your new definitions.

Give counterexamples of each, with sketches when feasible, that show how things could satisfy the less precise definitions but not match the intended terms.

you don't have to do all of them, thanks

Answer 1

Parabola:

Old definition: y=x^2

New definition: a U shaped graph

Counterexample: a "parabola" that extends straight up instead of sloping outwards

Answer 2

(Sorry if this ends up being formatted badly). So I would go with something like:

Triangle:

Old Definition: Blah blah blah your precise definition of a triangle

New Definition: A 2D shape made by connecting 3 points.

Then a counterexample to that would be a "triangle" made with wavy lines from point to point instead of straight lines. If that alone isn't enough to prove it, then show the angles of such a "triangle" might not sum to 180 degrees.