Concepts in Action: Equivalence between the trapezoid and T2

Age
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.