Name That Polygon

Date: 12/03/1999 at 13:36:18
From: Melissa Browne
Subject: What polygon is this?

Read each clue and then decide on the most specific name possible for 
the polygon being described.

1. It is a closed polygon with no parallel sides. It has no right 
   angles. All sides and angles are congruent. It has as many 
   diagonals as it has sides. Its diagonals form a star.

2. It is a closed polygon with two right angles. It has one pair of 
   parallel sides. It has only one line of symmetry. If you cut along 
   any one diagonal, you will create one triangle and one 
   quadrilateral.

I had a worksheet of about 30 of those, and these are the two that I 
am stuck on. They are probably somewhere between a triangle and a 
dodecagon.

Thank you.

Date: 12/04/1999 at 16:48:18
From: Doctor Jeremiah
Subject: Re: What polygon is this?

Here is some more detailed information about polygon number 1:

  >It is a closed polygon with no parallel sides.

It must have an odd number of sides.

  >All sides and angles are congruent. 

It is a regular polygon.

  >It has no right angles.

This information is redundant. There are no regular polygons with an 
odd number of sides and a right angle.

  >It has as many diagonals as it has sides.

A regular polygon with N sides has N(N-3)/2 diagonals. 

  >Its diagonals form a star. 

Most stars have five points. If the diagonals form a five pointed star 
and it has as many diagonals as it has sides, then how many sides does 
it have?


Here is some more detailed info about polygon number 2:

  >It is a closed polygon with two right angles.

It can't be a regular polygon because not all the angles are the same.

  >It has one pair of parallel sides. 

Only two opposite sides are parallel.

  >It has only one line of symmetry.

The top half and the bottom half are identical.

  >If you cut along any one diagonal, you will create one triangle 
  >and one quadrilateral. 

A quadrilateral has four sides and a triangle has three, so the total 
number of sides in the object must be five. (Seven minus the two sides 
formed by the diagonal.)


     +--parallel side-+
     |90               \
     |                  \
     |                   \
     |--line of symmetry--+
     |                   /
     |                  /
     |90               /
     +--parallel side-+


- Doctor Jeremiah, The Math Forum
  http://mathforum.org/dr.math/