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

From Karnataka Open Educational Resources

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