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

Hint 1

Hint 2

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Hint 6

Hint 7


Tangram Puzzle #2

Use the tangram pieces to form the following:

Hint 1

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Hint 7


Tangram Puzzle #3

Use the tangram pieces to form the following:

Hint 1

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Hint 7


Tangram Puzzle #4

Use the tangram pieces to form the following:

Hint 1

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Hint 7


Tangram Puzzle #5

Use the tangram pieces to form the following:

Hint 1

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Hint 7


Tangram Puzzle #6

Use the tangram pieces to form the following:

Hint 1

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Hint 7


Tangram Puzzle #7

Use the tangram pieces to form the following:

Hint 1

Hint 2

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Hint 6

Hint 7


Tangram Puzzle #8

Use the tangram pieces to form the following:

Hint 1

Hint 2

Hint 3

Hint 4

Hint 5

Hint 6

Hint 7

 


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