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