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### 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

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

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/
```
Associated Topics:
Elementary Geometry
Elementary Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons

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