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/