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Similar and congruent triangles (view source)

Revision as of 08:01, 29 April 2019

45,139 bytes removed , 08:01, 29 April 2019

→‎Concept Map

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[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]

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[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]

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[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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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].

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= Concept Map =

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=== Concept Map ===

__FORCETOC__

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[[File:similar_and_congruent_triangles.mm]]

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= ~~Textbook~~ =

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=== Additional Resources ===

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~~To add textbook links, please follow these instructions to:~~

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~~([{{fullurl:{{FULLPAGENAME}}/textbook|action~~=~~edit}} Click to create the subpage])~~

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=~~Additional Information~~=

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====OER====

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==~~Useful websites~~==

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*Web resources:

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==~~Reference Books~~==

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**This videos is related congruence of triangle.

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= ~~Teaching Outlines~~ =

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*Books and journals

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*Textbooks

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**NCERT Textbooks: [http://ncert.nic.in/textbook/pdf/gemh107.pdf#page=1&zoom=auto,-19,794 Class 7-Chapter 7:Congruence of Triangles] , [http://ncert.nic.in/textbook/textbook.htm?iemh1=7-15 Class 9: Triangles]

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*Syllabus documents

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====Non-OER====

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*Web resources:

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**[https://www.mathsisfun.com/geometry/triangles-congruent-finding.html Math is fun]

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*Books and journals

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*Textbooks:

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**Karnataka Govt Text book – Class 8 : [http://ktbs.kar.nic.in/new/website%20textbooks/class8/8th-english-maths-2.pdf Part 2]

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*Syllabus documents (CBSE, ICSE, IGCSE etc)

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=== Learning objectives ===

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=== Teaching Outlines ===

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#Congruent figures

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#Congruent triangles

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#Corresponding sides and corresponding angles of congruent triangles

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#Postulates for congruence of triangles

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====Concept # 1. Congruent triangles ====

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~~==Concept # 1. Congruent triangles ==~~

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~~===Learning objectives===~~

# Analyse and identify the structure of simple triangles

# Gather information about the similarities and differences between triangles

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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />

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*Process:

# The teacher can show the geogebra file and drag the vertices to obtain two triangles with the same dimensions and help them study the properties of congruent triangles.

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*Question Corner:

# List the properties of congruent triangles.

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*

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==~~=Activity No # ===~~

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====Concept # 2. Theorems related to congruency of triangles.====

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~~{| style="height:10px; float:right; align:center;"~~

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Any triangle is defined by six measures (three sides, three angles). Triangles are congruent if:

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~~|<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;">~~

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~~''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>~~

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|}

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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. Theorems related to congruency of triangles.==

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~~===Learning objectives~~===

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Any triangle is defined by six measures (three sides, three angles). Triangles are congruent if:~~<br>~~

# All three corresponding sides are equal in length. SSS (side side side) congruency postulate

# A pair of corresponding sides and the included angle are equal. -- SAS (side angle side) congruency postulate.

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# A pair of corresponding angles and a non-included side are equal.-- AAS (angle angle side) congruency postulate.

# HL (hypotenuse leg of a right triangle) :Two right triangles are congruent if the hypotenuse and one leg are equal.Also known as RHS postulate.

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~~===Notes for teachers===~~

===Activity No # 1. Congruency tests ===

{| style="height:10px; float:right; align:center;"

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*Website interactives/ links/ / Geogebra Applets

This geogebra file has been taken from www.geogebratube.org – 39142. file named "Conditions for congruent triangles" Shared by ayejatt.

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~~vsB2P6~~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" ~~enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true~~" />

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*Process:

# The teacher can use this geogebra file to explain and clarify the "tests for congruency" by moving the sliders.

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# Why SSA and AAA doesn't work ?

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==~~=Activity No # ===~~

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====Concept # 4.Similar triangles====

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~~{| style="height:10px; float:right; align:center;"~~

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~~|<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;">~~

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~~''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>~~

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|}

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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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~~===Activity No # ===~~

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~~{| style="height:10px; float:right; align:center;"~~

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~~|<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;">~~

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~~''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>~~

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|}

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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 # 4.Similar triangles==

===Learning objectives===

# To develop an intuitive understanding of the concept “similarity of figures”.

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*Multimedia resources: Laptop

*Website interactives/ links/ / Geogebra Applets

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<ggb_applet width="790" height="478" version="4.0" 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~~enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true~~" />

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*Process:

# The teacher can use this geogebra file to explain about similar triangles.

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# Discuss the applications of similar triangles in finding unknowns in real life situations.

# Give examples where one uses the concept of similarity.

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*

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==~~=Activity No # ===~~

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====Concept # 5. Similarity postulates/theorms====

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~~{| style="height:10px; float:right; align:center;"~~

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~~|<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;">~~

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~~''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>~~

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|}

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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 # 5. Similarity postulates/theorms==

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~~===Learning objectives~~===

Two triangles are said to be similar if any of the following equivalent conditions hold:

# The SSS similarity postulate states that if the sides of two triangles are in proportion, then the triangles are similar.

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# SAS Similarity Postulate states, “If an angle of one triangle is congruent to the corresponding angle of another triangle and the sides that include this angle are proportional, then the two triangles are similar.”

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~~===Notes for teachers===~~

===Activity No # Similarity test (AA postulate)===

{| style="height:10px; float:right; align:center;"

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*Multimedia resources :Laptop

*Website interactives/ links/ / Geogebra Applets

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enableRightClick="~~false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true~~" />

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*Process:

# The teacher can initially have a warm up session regarding terms congruence, similarity and corresponding angles and ratio.

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# Can the tree and its shadow be considered as similar figures ?

# Can this similarity concept be used to find the height and depth of objects ? Frame any two of your own questions which can be solved using similarity postulates.

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* ===== Solved problems/ key questions (earlier was hints for problems).[edit | edit source] ===== === Projects (can include math lab/ science lab/ language lab)[edit | edit source] === === Assessments - question banks, formative assessment activities and summative assessment activities ===

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===~~Activity No #~~ ===

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~~{| style="height:10px; float:right; align:center;"~~

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~~|<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;">~~

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~~''[http:~~/~~/karnatakaeducation~~.~~org.in/?q=node/305 Click to Comment~~]~~''</div>~~

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*Question Corner

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===~~Activity No #~~ ===

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~~{| style~~=~~"height:10px; float:right; align:center;"~~

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~~|<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;">~~

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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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*Website interactives/ links/ / Geogebra Applets

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*Question Corner

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===~~Activity No #~~ ===

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~~{| style~~=~~"height:10px; float:right; align:center;"~~

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~~|<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;">~~

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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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*Question Corner

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= ~~Hints for difficult problems~~ =

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= ~~Project Ideas =~~

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~~= Math Fun =~~

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~~'''Usage'''~~

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~~Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template~~

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Changes

Similar and congruent triangles (view source)

Revision as of 08:01, 29 April 2019

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