Math Is Fun Forum

Ava

Guest

Geometry Proofs

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

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Geometry Proofs

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

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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