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Line 4: − + − + − + − + − + − + − + − <mm>[[5a._Similar_and_Congruent_triangles.mm|Flash]]</mm> + + Line 42:
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Line 132: − − − = 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: − − − [[Image:KOER%20Triangles_html_m2f096af4.png]] − − − [[Image:KOER%20Triangles_html_4bd439df.png]] − − − − − '''Pythagoras' Theorem in − Three Dimensions''' − − − A − three-dimensional object can be described by three measurements - − length, width and height. − − − [[Image:KOER%20Triangles_html_679fe2f6.png]][[Image:KOER%20Triangles_html_m570261d2.png]] − − − We − can use Pythagoras' Theorem to find the length of the longest − straw that will fit inside − − − the − box or cylinder. − − − == GeoGebra Contributions == − # The GeoGebra file below to understand Similar Triangles <br> − ## Similar Triangles Part 1 http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_1.html − ## Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_1.ggb − ## Similar Triangles Part 2 http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_2.html − ## Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_2.ggb − ## Similar Triangles Part 3 http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_3.html − ## Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/Similar_Triangles_3.ggb − − − # The GeoGebra file below verifies the Thales theorem <br> − ## Thales Theorem http://www.karnatakaeducation.org.in/KOER/Maths/thales_theorem.html − ## Download ggb file here http://www.karnatakaeducation.org.in/KOER/Maths/thales_theorem.ggb − ## See a video that proves this theorem http://www.youtube.com/watch?v=Y-6yYsuGLoc
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|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
= Concept Map =
= Concept Map =
__FORCETOC__
__FORCETOC__
[[File:similar_ and _congruent triangles.mm|flash]]
= Textbook =
= Textbook =
To add textbook links, please follow these instructions to:
To add textbook links, please follow these instructions to:
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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* '''Estimated Time''' - 80 minutes (40 +40)
* '''Estimated Time''' - 80 minutes (40 +40)
* '''Prerequisites/Instructions, if any'''
* '''Prerequisites/Instructions, if any'''
* '''Multimedia resources'''
* '''Multimedia resources'''
[[Image:KOER%20Triangles_html_m3d25043b.jpg|300px|left]]<br><br>Suchetha . S. S Asst. Teacher ( Mathematics ) GJC Thyamagondlu. Nelamangala Talluk Bangalore Rural District doing the activity below on a lesson on similar triangles using GeoGebra in the classroom<br><br><br><br><br><br><br>
[[Image:KOER%20Triangles_html_m3d25043b.jpg|300px|left]]<br><br>Suchetha . S. S Asst. Teacher ( Mathematics ) GJC Thyamagondlu. Nelamangala Talluk Bangalore Rural District doing the activity below on a lesson on similar triangles using GeoGebra in the classroom<br><br><br><br><br><br><br><br>
* '''Website interactives/ links/ Geogebra Applets'''
* '''Website interactives/ links/ Geogebra Applets'''
* '''Process (How to do the activity)'''
* '''Process (How to do the activity)'''
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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* '''Estimated Time''' - 30 minutes
* '''Estimated Time''' - 30 minutes
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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* '''Estimated Time'''
* '''Estimated Time'''
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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* '''Estimated Time'''
* '''Estimated Time'''
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
