# Concepts in Action: Equivalence between the trapezoid and T2

## Contents

6-9.

### Materials

• From the triangular box: grey equilateral triangle
• From the small hexagonal box: yellow equilateral, three green equilateral triangles

### Presentation

1. Unite the three green triangles to form a trapezoid.
2. Knowing that each of these small triangles is congruent to the red triangle having the value of 1/4 T1, we can say that the trapezoid has the value of 3/4 T1.
3. The trapezoid can be superimposed on the grey equilateral triangle to show that 1/4 is lacking.
4. We've already seen that the red obtuse-angled triangle was equivalent to the small red equilateral triangle having the value of 1/4 T1.
5. So each green triangle would also be equivalent to a red obtuse-angled triangle.
6. These obtuse-angled triangles were each 1/3 of T2; T2 is composed of three obtuse-angled triangles having the value of 1/4 T1.
7. Therefore T2 is equal to 3/4 T1.
8. Having the same value of 3/4 T1, the trapezoid and T2 are equivalent.