A polygon is said to be convex if any line segment connecting two vertices of the polygon lies entirely inside the polygon. A polygon that is not convex is said to be concave. Convex Concave Prove, using induction on the number of vertices in the polygon, that the sum of the interior angles in a convex polygon with n vertices is (n - 2)n. You may assume interesting facts about triangles that you may remember from your past.

"for all natural numbers m, n, p, we have that if p | (m * n) then either p | m or p | n" Try different concrete values for m, n, and p. Is this a true statement or a false statement? If false, give a counterexample. If true, find a proof.

Prove in any Pythagorean triple (a, b, c) that either a or b is divisible by 3 and one of a, b, c is divisible by 5.

10) Use the contraposition to prove: a) If n +n+lis an even integer, then n is an odd integer. b) If x+y<10, then x<5v y<5.