Axiom 4: Things which coincide with one another are equal to one another
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From Euclid’s use of the word “equal” means “the same size”; two geometric figures are equal is justified by showing that one can be moved so that it coincides with the other.
Objectives
To demonstrate things which coincide with one another are equal to one another
Estimated Time
15 minutes
Prerequisites/Instructions, prior preparations, if any
Prior knowledge of points, lines and shapes
Materials/ Resources needed
- Digital : Computer, geogebra application, projector.
- Non digital : Worksheet and pencil
- Geogebra files : “Axiom-4a.ggb” "Axiom-4b.ggb” “Axiom-4c.ggb”
Download this geogebra file from this link.
Download this geogebra file from this link.
Download this geogebra file from this link.
Process (How to do the activity)
- The files demonstrate Euclid's fourth axiom.
- If a line coincides with another are they equal.
- If a circle coincides with another are they equal.
- If a pentagon coincides with another are they equal.
Evaluation at the end of the activity
- What are the parameters that should match for things to be equal