Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**Ava****Guest**

A square has 2 diagonals. (proofs)

A. given

B. unfounded

C. definition of an octagon

D. The number of diagonals is (n-3)n/2, where N is the number of size, which is four for a square

E. 1267200 inches

F. definition of supplementary angles

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,829

hi Ava

Welcome to the forum.

Is that really a question you have been set? Just multi choice with those alternatives.

Instead I'll try to teach you something useful.

Let's say a convex polygon has N sides. By convex I mean that the diagonals are always inside the shape.

From one vertex you can make N-3 diagonals. N, less 1 for the point itself, less 2 for the neighbouring vertices as joining the point to those doesn't make a diagonal.

As there are N vertices you can make N times (N-3) diagonals like this … but … every diagonal is counted twice, once A to B, and then again, B to A. So divide by two to eliminate repeats.

So the formula for the number of diagonals in any convex polygon is

where N is the number of vertices.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

Offline

Pages: **1**