# Tangrams

#### Tangrams puzzles are said to be the "The Chinese
Puzzle". It can be dated back as far as 1813 and was considered
a game in China for women and children.

#### A Tangram puzzle is a puzzle that shows how seven
particular pieces that make up a standard square can be translated,
reflected, and rotated to form other interesting shapes that have
a particular property in common.

#### The classic rules are you must use all seven pieces
(tans), they must touch and none may overlap

#### The seven pieces that are given are two small congruent
triangles, a medium triangle, two large congruent triangles, a
square and a parrallogram. These seven pieces make up an equilateral
square

#### Before we begin playing let's investigate how the
pieces are created and how they relate...as the size and relation
of the pieces are critical to success of the game.

#### Pieces of a Tangram Puzzle

#### As stated earlier, we start out with an equilateral
square...the exact dimension does not matter as long as it is
equilateral.

#### To get our medium triangle find the midpoint of side
AB, label it Q,and side BC, label it V, then construct segment
QC joining the midpoints.

#### This gives us our medium triangle...Now we will construct
our two large triangles.

#### Construct a diagonal from pt A to pt C. Next find
the midpoint of the diagonal, pt X, and construct segment DX

#### This gives us our two large triangles...Next we'll
construct our parrallogram

#### Construct the midpoint of QV, pt H, and the midpoint
of AX, pt W; then construct segment WH

#### Thus we have our parrallogram...from here we can construct
one of our small triangles

#### All you have to do is construct segment XH

#### Now it is easy to get our last two pieces, the square
and our other small triangle (which is congruent to the triangle
we just constructed)

#### Locate the midpoint of segment XC, pt Y, and construct
segment YV.

####

#### Take the time to explore these shapes a little more
and come up with some conjectures about them. Maybe look at the
relations of the areas.

#### Now let's experiment with our pieces and try our hand
at a couple of puzzles.

#### To use the pieces click on the pieces to translate
them from one place to another. Using the arrow on the red points
on each piece allows you to rotate the pieces...if you need to
reflect the piece you have to use the menu of GSP

#### Tangram Puzzle #1

#### Use the tangram pieces
to form the following:

#### If you get stuck here are a few hints

#### Tangram Puzzle #2

#### Use the tangram pieces
to form the following:

#### Tangram Puzzle #3

#### Use the tangram pieces
to form the following:

#### Tangram Puzzle #4

#### Use the tangram pieces
to form the following:

#### Tangram Puzzle #5

#### Use the tangram pieces
to form the following:

#### Tangram Puzzle #6

#### Use the tangram pieces
to form the following:

#### Tangram Puzzle #7

#### Use the tangram pieces
to form the following:

#### Tangram Puzzle #8

#### Use the tangram pieces
to form the following:

####