# Concepts in Action: Equivalence between two rhombi

## Contents

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.