Difference between revisions of "Axiom 2 and 3: If equals are added or subtracted to equals, the wholes are equal"

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===Name of the activity===
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Euclid, magnitudes are objects that can be compared, added, and subtracted, provided they are of the “same kind.” Addition or elimination of equal parameters to equal quantities results in equal things, for which the relation of equality and the operation of subtraction make sense. In Euclid’s mathematics this relation and this operation apply not only to straight segments and numbers but also to geometrical objects.
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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 ===
 
=== Objectives ===
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To demonstrate things which are equal to the same thing are equal to one another
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* To demonstrate if equals are added to equals, the wholes are equal
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* To demonstrate if equals are subtracted to equals, the wholes are equal
  
 
===Estimated Time===
 
===Estimated Time===
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=== Prerequisites/Instructions, prior preparations, if any ===
 
=== Prerequisites/Instructions, prior preparations, if any ===
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Prior knowledge of point, lines, angles, parallel lines
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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
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* Geogebra files : “[https://ggbm.at/w5abppzb Axiom-1.ggb]”
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* Geogebra files : “[https://ggbm.at/uzpcnm89 Axiom-2 and 3.ggb]”
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{{Geogebra|w5abppzb}}
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{{Geogebra|uzpcnm89}}
  
 
===Process (How to do the activity)===
 
===Process (How to do the activity)===
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* The file demonstrates the first Euclid's axiom.
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* The file demonstrates the Euclid's second and third axiom.
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* The measures of all the lines corresponds to the distance between 0 of x-axis to point F.
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* The measures of all the lines corresponds to the distance between 0 of x-axis to point F.
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* 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'''.
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* 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'''.
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* Since  all the lines measure the same distance (0 to point F), the lines are equal to each other.
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* With the change in position of slider '''Equals2''' an equal length of 3 is added to all lines.
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* Record the segment lengths in the worksheet
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* It can be observed that the length of all the lines correspondingly increases.
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: {| class="wikitable"
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* What do you notice about the lines.
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|Position   of Distance
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* Again changing the position of slider '''Equals2''' to 0 the measure of 3 units is eliminated.
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|0   - Point F
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* Now what do you notice about the lines.
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|Length   BC
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* Record the segment lengths in the worksheet
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|Length   GH
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:{| class="wikitable"
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|Length   DE
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|Position of '''Equals2'''
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|Length   IJ
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|0 - Point F
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|Length BC
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|Length GH
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|Length EF
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|Length IJ
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|Length of the line + position of '''Equals 2'''
 
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|-
 
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|.
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'''Evaluation at the end of the activity'''
 
'''Evaluation at the end of the activity'''
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* Can you conclude if all the lines are equal to a measure on x- axis then they are equal to one another.
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* Can you conclude if equal measures are added to equal lines the resulting lines are equal.
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[[Category:Introduction to Euclid's Geometry]]

Latest revision as of 08:14, 29 October 2019

Euclid, magnitudes are objects that can be compared, added, and subtracted, provided they are of the “same kind.” Addition or elimination of equal parameters to equal quantities results in equal things, for which the relation of equality and the operation of subtraction make sense. In Euclid’s mathematics this relation and this operation apply not only to straight segments and numbers but also to geometrical objects.

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.
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