# Axiom 1: Things which are equal to the same thing are equal to one another

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Comparison of geometric parameters to check for their equality, for example if an area of a triangle equals the area of a rectangle and the area of the rectangle equals that of a square, then the area of the triangle also equals the area of the square.

### Objectives

To demonstrate things which are equal to the same thing are equal to one another

### Estimated Time

15 minutes

### Prerequisites/Instructions, prior preparations, if any

Prior knowledge of points and lines

### Materials/ Resources needed

- Digital : Computer, geogebra application, projector.
- Non digital : Worksheet and pencil
- Geogebra files : “Axiom-1.ggb”

Download this geogebra file from this link.

### Process (How to do the activity)

- The file demonstrates the first Euclid's axiom.
- The measures of all the lines corresponds to the distance between 0 of x-axis to point F.
- If the distance of point F from 0 is increased or decreased the lengths of all the lines also varies accordingly this can be done by using the slider
**Distance**. - Since all the lines measure the same distance (0 to point F), the lines are equal to each other.
- Record the segment lengths in the worksheet

Position of Distance 0 - Point F Length BC Length GH Length DE Length IJ . .

**Evaluation at the end of the activity**

- Can this be extended to other geometric shapes