Tangram: Side Lengths

Topic:Isosceles Triangles, Parallelogram, Pythagoras or Pythagorean Theorem, Right Triangles, Square, Triangles

You have discovered that all the triangle pieces of the Tangram are right and isosceles, therefore the measures of their internal angles are 90°, 45°, 45°, while the parallelogram has two internal angles that measure 45° and two that measure 135°, and the square by definition has all right angles. If the length of the side of the square is 1 unit, calculate the lengths of the sides of all the pieces of the Tangram. Check your results by selecting the sides of the Tangram's pieces in the app below.

Have you applied any theorem or property to calculate the sides lengths? Explain.

Compare the lengths of the leg of the large triangle and of the hypotenuse of the medium triangle. Which of these statements is true?

Select all that apply

A
The leg of the large triangle is longer than the hypotenuse of the medium triangle
B
The leg of the large triangle is shorter than the hypotenuse of the medium triangle
C
The leg of the large triangle and the hypotenuse of the medium triangle have the same length
D
The two lengths are not commensurable

Check my answer (3)

Compare the lengths of the leg of the medium triangle and of the diagonal of the square. Which of these statements is true?

Select all that apply

A
The leg of the medium triangle is longer than the diagonal of the square
B
The leg of the medium triangle is shorter than the diagonal of the square
C
The leg of the medium triangle and the diagonal of the square have the same length
D
The two lengths are not commensurable

Check my answer (3)

Find a pair of sides of the Tangram pieces (also not belonging to the same piece), whose lengths are not commensurable.

Check my answer

Tangram: Side Lengths

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