Concepts in Action: Equivalence between two rhombi

Age
6-9.

Materials

 * From the small hexagonal box: two red obtuse-angled and two red equilateral triangles
 * From the triangular box: grey equilateral, green right- angled 2/2 triangle fraction insets (optional)

Presentation

 * 1) Join each pair of red triangles along the black lines to form two rhombi.
 * 2) Superimpose one rhombus on the other to show congruency.
 * 3) Demonstrate that each rhombus was divided into two equal pieces.
 * 4) Since each triangle has the value of 1/2 of the same rhombus, all of the triangles are equivalent.
 * 5) Demonstrate this equivalence sensorially by superimposing the two metal inset pieces on first one red triangle, and then in another arrangement on the other.
 * 6) We know that the red equilateral triangle has the value of 1/4 T1.
 * 7) Since the red obtuse-angled triangle is equivalent, it must also have the value of 1/4.
 * 8) Therefore, 1/4 + 1/4 = 1/2 T1.
 * 9) Superimpose the green right-angled triangle as a proof.
 * 10) Following this line, the grey triangle can be constructed with two rhombi.
 * 11) Also this 1/2 is the difference between the two hexagons in the form of a rhombus or this right-angled scalene triangle.