Axiom 2 and 3: If equals are added or subtracted to equals, the wholes are equal
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Name of the activity
Brief blurb describing what the activity. If this has been borrowed from some external web site (for example, a non OER or OER site which had this idea and based on which the activity was developed)
Objectives
- To demonstrate if equals are added to equals, the wholes are equal
- To demonstrate if equals are subtracted to equals, the wholes are equal
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-2 and 3.ggb”
Download this geogebra file from this link.
Process (How to do the activity)
- The file demonstrates the Euclid's second and third 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 Equals1.
- With the change in position of slider Equals2 an equal length of 3 is added to all lines.
- It can be observed that the length of all the lines correspondingly increases.
- What do you notice about the lines.
- Again changing the position of slider Equals2 to 0 the measure of 3 units is eliminated.
- Now what do you notice about the lines.
- Record the segment lengths in the worksheet
Position of Equals2 0 - Point F Length BC Length GH Length EF Length IJ Length of the line + position of Equals 2 . .
Evaluation at the end of the activity
- Can you conclude if equal measures are added to equal lines the resulting lines are equal.