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Axiom 2 and 3: If equals are added or subtracted to equals, the wholes are equal (view source)
Revision as of 12:04, 24 April 2019
, 12:04, 24 April 2019no edit summary
=== Objectives ===
=== Objectives ===
To demonstrate things which are equal to the same thing are equal to one another
* 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===
===Estimated Time===
=== Prerequisites/Instructions, prior preparations, if any ===
=== Prerequisites/Instructions, prior preparations, if any ===
Prior knowledge of point, lines, angles, parallel lines
Prior knowledge of points and lines
===Materials/ Resources needed===
===Materials/ Resources needed===
* Digital : Computer, geogebra application, projector.
* Digital : Computer, geogebra application, projector.
* Non digital : Worksheet and pencil
* Non digital : Worksheet and pencil
* Geogebra files : “[https://ggbm.at/w5abppzb Axiom-1.ggb]”
* Geogebra files : “[https://ggbm.at/w5abppzb Axiom-2 and 3.ggb]”
{{Geogebra|w5abppzb}}
{{Geogebra|w5abppzb}}
===Process (How to do the activity)===
===Process (How to do the activity)===
* The file demonstrates the first Euclid's axiom.
* 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.
* 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'''.
* 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'''.
* Since all the lines measure the same distance (0 to point F), the lines are equal to each other.
* With the change in position of slider '''Equals2''' an equal length of 3 is added to all lines.
* Record the segment lengths in the worksheet
* It can be observed that the length of all the lines correspondingly increases.
: {| class="wikitable"
* What do you notice about the lines.
|Position of Distance
* Again changing the position of slider '''Equals2''' to 0 the measure of 3 units is eliminated.
|0 - Point F
* Now what do you notice about the lines.
|Length BC
* Record the segment lengths in the worksheet
|Length GH
:{| class="wikitable"
|Length DE
|Position of '''Equals2'''
|Length IJ
|0 - Point F
|Length BC
|Length GH
|Length EF
|Length IJ
|Length of the line + position of '''Equals 2'''
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'''Evaluation at the end of the activity'''
'''Evaluation at the end of the activity'''
* Can you conclude if all the lines are equal to a measure on x- axis then they are equal to one another.
* Can you conclude if equal measures are added to equal lines the resulting lines are equal.