# Concepts in Action: Equivalence between two rhombi

From wikisori

## Contents

### 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)

### Preparation

### Presentation

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

### Control Of Error

### Points Of Interest

### Purpose

### Variation

### Links

### Handouts/Attachments