Difference between revisions of "Basics of Geometry"

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<!-- This portal was created using subst:box portal skeleton  -->''[http://karnatakaeducation.org.in/KOER/index.php/%E0%B2%B0%E0%B3%87%E0%B2%96%E0%B2%BE%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%E0%B2%A6_%E0%B2%AA%E0%B2%B0%E0%B2%BF%E0%B2%9A%E0%B2%AF ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''<!--        http://karnatakaeducation.org.in/KOER/index.php/ರೇಖಾಗಣಿತದ_ಪರಿಚಯ       -->
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[http://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]
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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://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://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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[http://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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[http://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://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://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://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
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= Concept Map =
 
= Concept Map =
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<mm>[[Geometry.mm|Flash]]</mm>
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[[File:Geometry.mm|Flash]]
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__FORCETOC__
 
__FORCETOC__
 
= Textbook =
 
= Textbook =
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To add textbook links, please follow these instructions to:  
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To add textbook links, please follow these instructions to: ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
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([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
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#[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter13.pdf Karnataka text book for Class 10, Chapter 13 - Basic Geometry]
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=Additional Information=
 
=Additional Information=
 
==Useful websites==
 
==Useful websites==
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#[http://www.onlinemathlearning.com/basic-geometry.html Very Basic concepts on Geometry]
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#[http://www.msc.uky.edu/droyster/courses/fall11/MA341/Classnotes/Chapter%2001-The%20Origins%20of%20Geometry.pdf origin of geometry]
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In addition to basic ideas there are videos.
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#[http://www.msc.uky.edu/droyster/courses/fall11/MA341/Classnotes/Chapter%2001-The%20Origins%20of%20Geometry.pdf origin of geometry]
 
==Reference Books==
 
==Reference Books==
  
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===Learning objectives===
 
===Learning objectives===
 
===Notes for teachers===
 
===Notes for teachers===
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===Activity No 1 : Angles formed when a transversal intersects parallel lines ===
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===Activity No 1 : [[Angles formed when a transversal intersects parallel lines|Angles formed when a transversal intersects parallel line]]    ===
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
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*'''Estimated Time''' : <br>
 
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90 minutes
 
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*'''Materials/ Resources needed''' :<br>
 
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Laptop, geogebra file, projector and pointer.
 
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*'''Prerequisites/Instructions, if any''' :  <br>
 
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#The students should have prior knowledge of parallel lines , transversal, angles and types of angles formed when a pair of parallel lines are intersected by a transversal.
 
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#They should know what the terms interior, exterior, adjacent, alternate, consecutive, congruent, linear and corresponding mean.
 
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#Students should know the definition of complementary angles, supplementary angles, and congruent angles.
 
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*'''Multimedia resources''' :
 
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Laptop
 
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*Website interactives/ links/ / Geogebra Applets : <br>
 
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[[File:4..png|400px]]
 
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*'''Process''': <br>
 
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#Reiterate that when a transversal  intersects parallel lines, several pairs of congruent and supplementary angles are formed.
 
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#Have students draw two parallel lines and a third line(transversal) intersecting those two lines on their own paper. Direct them to think about any angle relationships they see. Have them discuss their conjectures with a partner.
 
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#The teacher can next  project the GeoGebra worksheet and discuss about types of angles and their relationships with the class .
 
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#Finally the teacher and students can summarize together the angle relationships.<br>
 
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Linear pair of angles - adjacent and supplementary<br>
 
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Vertical angles - congruent<br>
 
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Corresponding angles -congruent<br>
 
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Alternate interior angles - congruent<br>
 
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Same side interior angles - supplementary<br>
 
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Alternate exterior angles - congruent<br>
 
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Same side exterior angles - supplementary<br>
 
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*'''Developmental Questions (What discussion questions)'''  : <br>
 
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#How many pairs of corresponding angles are there ?
 
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#What is true about corresponding angles formed when parallel lines are cut by a transversal?
 
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#Compare different pairs of alternate interior angles. What do you notice?
 
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#<EGD and <AHF are alternate exterior angles. What is another pair of alternate exterior angles?
 
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#Compare different pairs of same-side interior angles. What do you notice?
 
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#Compare different pairs of same-side exterior angles. What do you notice?
 
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*'''Evaluation (Questions for assessment of the child)''' : <br>
 
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#What are the characteristics of linear angles (adjacent and supplementary) ?
 
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#What do you observe about the angle measures of the linear angles?
 
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*'''Question Corner''' :
 
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#What do adjacent , alternate, linear , corresponding and consecutive mean individually
 
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#What are complementary angles?
 
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#What are supplementary angles ?
 
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#What does it mean if two angles are congruent?
 
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#What is the complement of 65 degrees
 
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#What is the supplement of 70 degrees?
 
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#Compare angle relationships formed by parallel lines vs. angle relationships formed by non-parallel lines.
 
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===Activity No # ===
 
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
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*Estimated Time
 
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*Materials/ Resources needed
 
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*Prerequisites/Instructions, if any
 
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*Multimedia resources
 
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*Website interactives/ links/ / Geogebra Applets
 
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*Process/ Developmental Questions
 
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*Evaluation
 
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*Question Corner
 
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==Concept #2 ==
 
==Concept #2 ==
 
===Learning objectives===
 
===Learning objectives===
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*Evaluation
 
*Evaluation
 
*Question Corner
 
*Question Corner
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= Math Fun =
 
= Math Fun =
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==Teachers Corner==
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===GeoGebra Contributions===
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#The GeoGebra file below demonstrates properties of consecutive interior angles
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##consecutive interior angles http://karnatakaeducation.org.in/KOER/Maths/consecutive_angles.html
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##Download ggb file here http://karnatakaeducation.org.in/KOER/Maths/consecutive_angles.ggb
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##See a video to understand this better http://www.youtube.com/watch?v=cbMwDB1A1rA
  
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'''Usage'''
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#The GeoGebra file below demonstrates that corresponding angles are congruent
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##corresponding angles http://karnatakaeducation.org.in/KOER/Maths/Parallel_lines.html
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##Download ggb file here http://karnatakaeducation.org.in/KOER/Maths/Parallel_lines.ggb
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##See a video to understand this better http://www.youtube.com/watch?v=hFIjoDPxPdk
  
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[[Category:Basics of Geometry]]
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--[[User:Ranjani|Ranjani]] ([[User talk:Ranjani|talk]]) 02:21, 12 September 2013 (PDT)
 

Latest revision as of 22:29, 19 April 2020

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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

[maximize]


Textbook

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

  1. Karnataka text book for Class 10, Chapter 13 - Basic Geometry

Additional Information

Useful websites

  1. Very Basic concepts on Geometry
  2. origin of geometry

In addition to basic ideas there are videos.

  1. origin of geometry

Reference Books

Teaching Outlines

Concept #1

Learning objectives

Notes for teachers

Activity No 1 : Angles formed when a transversal intersects parallel line

Concept #2

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #3

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner


Hints for difficult problems

Project Ideas

Math Fun

Teachers Corner

GeoGebra Contributions

  1. The GeoGebra file below demonstrates properties of consecutive interior angles
    1. consecutive interior angles http://karnatakaeducation.org.in/KOER/Maths/consecutive_angles.html
    2. Download ggb file here http://karnatakaeducation.org.in/KOER/Maths/consecutive_angles.ggb
    3. See a video to understand this better http://www.youtube.com/watch?v=cbMwDB1A1rA
  1. The GeoGebra file below demonstrates that corresponding angles are congruent
    1. corresponding angles http://karnatakaeducation.org.in/KOER/Maths/Parallel_lines.html
    2. Download ggb file here http://karnatakaeducation.org.in/KOER/Maths/Parallel_lines.ggb
    3. See a video to understand this better http://www.youtube.com/watch?v=hFIjoDPxPdk
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