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.


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