Difference between revisions of "Similarity and Congruence"

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(Created page with "{{subst:Math-Content}} == Evaluation == == Self-Evaluation == == Further Explorations == == Enrichment Activities == = Pythagorean Theorem = Pythagoras' Theorem was...")
 
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= Concept Map =
 
= Concept Map =
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<mm>[[5a._Similar_and_Congruent_triangles.mm|Flash]]</mm>
 
__FORCETOC__
 
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= Textbook =
 
= Textbook =
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= Teaching Outlines =
 
= Teaching Outlines =
  
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==Concept #==
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==Concept #1 - Understanding similarity==
 
===Learning objectives===
 
===Learning objectives===
 +
#To show similar planar figures, discuss congruence and properties of congruent/ similar triangles
 +
 
===Notes for teachers===
 
===Notes for teachers===
 
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
 
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
  
−
===Activity No # ===
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===Activity No #1 ===
 
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
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 +
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 +
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==== Material and Resources Required ====
 +
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Blackboard
 +
 +
 +
Geogebra files +
 +
projector
 +
 +
 +
Calculator
 +
 +
 +
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'''[[Pre-requisites/Instructions]] '''
 +
 +
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* Planar figures and triangles
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* Draw pairs of figures on the board [ both similar and dissimilar]; they can identify overlap of congruent figures
 +
* Ask the children to identify
 +
* If the children know the names of the theorem, ask them to explain- ask them what is SSS, AAA, ASA
 +
* Show ratio and give the idea of proportionality
 +
* Geogebra files. When I change the sides/ proportion, the triangles change in size. But the proportion remains the same, angle remains the same
 +
* With calculator they verify proportion (this is very very useful for involving the whole class) they all can see the proportion remains constant though the size changes
 +
* Show the arithmetic behind the proportion
 +
 +
==== Evaluation ====
 +
 +
[Activity evaluation -
 +
What should the teacher watch for when you do the activity; based on
 +
what they know change]
 +
 +
 +
* Confusion between congruence and similarity
 +
* When they give the theorem, if they cannot identify included side and angle
 +
* When there is a wrong answer, identify what is the source of the confusion – sides, ratio and proportion
 +
 +
* Direct substitution
 +
 +
 
* '''Estimated Time'''
 
* '''Estimated Time'''
 
* '''Materials/ Resources needed'''
 
* '''Materials/ Resources needed'''
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= References =
 
= References =
 +
== Enrichment    Activities ==
 +
 
 +
=== Activity 2 Similar Triangles ===
 +
 +
'''Learning Objective'''
 +
 +
 +
To show similar planar
 +
figures, discuss congruence and properties of congruent/ similar
 +
triangles
 +
 +
 +
 +
 +
 +
==== Material and Resources Required ====
 +
 +
Blackboard
 +
 +
 +
Geogebra files +
 +
projector
 +
 +
 +
Calculator
 +
 +
 +
 +
'''[[Pre-requisites/Instructions]] '''
 +
 +
 +
* Planar figures and triangles
 +
* Draw pairs of figures on the board [ both similar and dissimilar]; they can identify overlap of congruent figures
 +
* Ask the children to identify
 +
* If the children know the names of the theorem, ask them to explain- ask them what is SSS, AAA, ASA
 +
* Show ratio and give the idea of proportionality
 +
* Geogebra files. When I change the sides/ proportion, the triangles change in size. But the proportion remains the same, angle remains the same
 +
* With calculator they verify proportion (this is very very useful for involving the whole class) they all can see the proportion remains constant though the size changes
 +
* Show the arithmetic behind the proportion
 +
 +
==== Evaluation ====
 +
 +
[Activity evaluation -
 +
What should the teacher watch for when you do the activity; based on
 +
what they know change]
 +
 +
 +
* Confusion between congruence and similarity
 +
* When they give the theorem, if they cannot identify included side and angle
 +
* When there is a wrong answer, identify what is the source of the confusion – sides, ratio and proportion
 +
 +
* Direct substitution

Revision as of 02:01, 6 December 2013

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

While creating a resource page, please click here for a resource creation checklist.

Concept Map

Error: Mind Map file 5a._Similar_and_Congruent_triangles.mm not found


Textbook

To add textbook links, please follow these instructions to: (Click to create the subpage)

Additional Information

Useful websites

Reference Books

Teaching Outlines

Concept #1 - Understanding similarity

Learning objectives

  1. To show similar planar figures, discuss congruence and properties of congruent/ similar triangles

Notes for teachers

These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.

Activity No #1





Material and Resources Required

Blackboard


Geogebra files + projector


Calculator


Pre-requisites/Instructions


  • Planar figures and triangles
  • Draw pairs of figures on the board [ both similar and dissimilar]; they can identify overlap of congruent figures
  • Ask the children to identify
  • If the children know the names of the theorem, ask them to explain- ask them what is SSS, AAA, ASA
  • Show ratio and give the idea of proportionality
  • Geogebra files. When I change the sides/ proportion, the triangles change in size. But the proportion remains the same, angle remains the same
  • With calculator they verify proportion (this is very very useful for involving the whole class) they all can see the proportion remains constant though the size changes
  • Show the arithmetic behind the proportion

Evaluation

[Activity evaluation - What should the teacher watch for when you do the activity; based on what they know change]


  • Confusion between congruence and similarity
  • When they give the theorem, if they cannot identify included side and angle
  • When there is a wrong answer, identify what is the source of the confusion – sides, ratio and proportion
  • Direct substitution


  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ Geogebra Applets
  • Process (How to do the activity)
  • Developmental Questions (What discussion questions)
  • Evaluation (Questions for assessment of the child)
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ Geogebra Applets
  • Process (How to do the activity)
  • Developmental Questions (What discussion questions)
  • Evaluation (Questions for assessment of the child)
  • Question Corner


Concept #

Learning objectives

Notes for teachers

These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ Geogebra Applets
  • Process (How to do the activity)
  • Developmental Questions (What discussion questions)
  • Evaluation (Questions for assessment of the child)
  • Question Corner


Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ Geogebra Applets
  • Process (How to do the activity)
  • Developmental Questions (What discussion questions)
  • Evaluation (Questions for assessment of the child)
  • Question Corner

Hints for difficult problems

Project Ideas

Math Fun

Usage

Create a new page and type {{subst:Math-Content}} to use this template


Evaluation

Self-Evaluation

Further Explorations

Enrichment Activities

Pythagorean Theorem

Pythagoras' Theorem was discovered by Pythagoras, a Greek mathematician and philosopher who lived between approximately 569 BC and 500 BC.


Pythagoras' Theorem states that:


In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is:


KOER Triangles html m2f096af4.png


KOER Triangles html 4bd439df.png



Pythagoras' Theorem in Three Dimensions


A three-dimensional object can be described by three measurements - length, width and height.


KOER Triangles html 679fe2f6.pngKOER Triangles html m570261d2.png


We can use Pythagoras' Theorem to find the length of the longest straw that will fit inside


the box or cylinder.


Evaluation

Self-Evaluation

Further Explorations

Enrichment Activities

See Also

Teachers Corner

Suchetha . S. S Asst. Teacher ( Mathematics ) GJC Thyamagondlu. Nelamangala Talluk Bangalore Rural District doing a lesson on similar triangles using GeoGebra in the classroom

KOER Triangles html m3d25043b.jpg


GeoGebra Contributions

  1. The GeoGebra file below to understand Similar Triangles
    1. Similar Triangles Part 1 http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_1.html
    2. Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_1.ggb
    3. Similar Triangles Part 2 http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_2.html
    4. Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_2.ggb
    5. Similar Triangles Part 3 http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_3.html
    6. Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_3.ggb
    7. See a video to understand this concept http://www.youtube.com/watch?v=BI-rtfZVXy0
  1. The GeoGebra file below verifies the Thales theorem
    1. Thales Theorem http://www.karnatakaeducation.org.in/KOER/Maths/thales_theorem.html
    2. Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/thales_theorem.ggb
    3. See a video that proves this theorem http://www.youtube.com/watch?v=Y-6yYsuGLoc

Books

References

Enrichment Activities

Activity 2 Similar Triangles

Learning Objective


To show similar planar figures, discuss congruence and properties of congruent/ similar triangles



Material and Resources Required

Blackboard


Geogebra files + projector


Calculator


Pre-requisites/Instructions


  • Planar figures and triangles
  • Draw pairs of figures on the board [ both similar and dissimilar]; they can identify overlap of congruent figures
  • Ask the children to identify
  • If the children know the names of the theorem, ask them to explain- ask them what is SSS, AAA, ASA
  • Show ratio and give the idea of proportionality
  • Geogebra files. When I change the sides/ proportion, the triangles change in size. But the proportion remains the same, angle remains the same
  • With calculator they verify proportion (this is very very useful for involving the whole class) they all can see the proportion remains constant though the size changes
  • Show the arithmetic behind the proportion

Evaluation

[Activity evaluation - What should the teacher watch for when you do the activity; based on what they know change]


  • Confusion between congruence and similarity
  • When they give the theorem, if they cannot identify included side and angle
  • When there is a wrong answer, identify what is the source of the confusion – sides, ratio and proportion
  • Direct substitution
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