Concepts in Action: Relationship between T1 and T2

Age

6-9.

Presentation

1. With the pieces of the small hexagonal box, form various figure: hexagon, trapezoid, rhombus, and equilateral triangle and hexagon.
2. Superimpose the grey hexagon on the red and yellow hexagon to demonstrate congruency.
3. Recall the value relationships already established.
4. Since the equilateral triangle is equal to 1/2 the red hexagon, then it is also equal to 1/2 of the grey hexagon - or a trapezoid.
5. Bring from the triangular box the grey unit triangle (T1) and the four small red equilateral triangles (T3).
6. We know that the yellow triangle T2 is equivalent to the trapezoid which is 1/2 of the grey hexagon.
7. One of the triangles of the trapezoid is congruent to one of the small red equilateral triangles (T3).
8. Superimpose them.
9. Thus, one red triangle is 1/3 of the trapezoid.
10. The red triangle as we know is 1/4 of the large grey unit triangle (T1).
11. Four of these red triangles are equivalent to the grey unit triangle.
12. Because the yellow triangle (T2) is made up of three of the small red triangles (T3), then we can say that the yellow triangle (T2) is made up of 3/4 (T3) of the grey unit triangle (T2 = 3/4 T1).