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

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(Created page with "===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...")
 
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=== 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
+
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]”
+
* 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)===
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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
 +
|Length GH
 +
|Length EF
 +
|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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|.
 
|.
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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.

Revision as of 06:34, 24 April 2019

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.
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