# 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

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

### 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