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### Dividing a 30-60-90 Triangle in Four

```
Date: 08/07/99 at 12:07:01
From: Jessica Smith
Subject: Dividing a 30-60-90 triangle

I need to divide a 30-60-90 triangle into 4 triangles similar to the
first triangle with each one having 1/4th of the area. I also need to
find 4 different ways to divide it. I have found 2 ways as below, but
I need to find 2 more ways and I am having a lot of trouble with it.

|\                    |\
| \                   | \
|  \                  |  \
|   \                 |   \
|    \                |    \
|  A  \               |  A  \
|      \              |      \
|_______\             |_______\
|       |\            |       |\
|      /| \           |\      | \
|  B  / |  \          | \  B  |  \
|    /  |   \         |  \    |   \
|   /   |    \        |   \   |    \
|  /  C |  D  \       | C  \  |  D  \
| /     |      \      |     \ |      \
|/______|_______\     |______\|_______\

Other than these two ways I can't figure it out.

Thanks,
Jessica
```

```
Date: 08/07/99 at 17:41:22
From: Doctor Tom
Subject: Re: dividing a 30-60-90 triangle

Hi Jessica,

You're almost there. Take a look at the two triangles labeled C and D
on the bottom of your first figure. They form a 60-60-60 equilateral
triangle, don't they? How many ways can you divide a 60-60-60 triangle
into two 30-60-90 triangles?

- Doctor Tom, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons

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