Tangram Worksheet

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K-12: Materials at high school level.


A square with the tangram pieces

In the square above we see several pieces:

  • Two squares - S1 and S2
  • Four triangles - T1, T2, T3, and T4
  • One parallelogram - P

Materials: One set of tangram pieces to experiment with.


1. Are the squares congruent or similar? ______________________________


2. The triangles are not all congruent, but they do pair up.

_______ is congruent to _____, and _____ is congruent to ______


3. Name two triangles that are similar but NOT congruent:

_____ and _____


4. If we put T1 and T2 together along the longest side it will look like a square. Which square will T1 plus T2 be congruent to? _______


5. You can arrange S2 and the small triangles T3 and T4 so that they combine in a shape congruent to P. Draw a picture below to show how to put S2, T3 and T4 together.








6. If we put S1, T1 and T2 together in a similar way, do we get a similar shape or a congruent one? ____________________


7. We can also form P from the triangles T1 and T2. Draw a picture below showing how to put the triangles together.