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From Karnataka Open Educational Resources

Similar and congruent triangles (view source)

Revision as of 08:30, 29 April 2019

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→‎Concept 1: Identify congruent shapes
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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]
 
**Karnataka Govt Text book – Class 8 :  [http://ktbs.kar.nic.in/new/website%20textbooks/class8/8th-english-maths-2.pdf Part 2]
 
*Syllabus documents (CBSE, ICSE, IGCSE etc)
 
*Syllabus documents (CBSE, ICSE, IGCSE etc)
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=== Teaching Outlines ===
      
=== Learning objectives ===
 
=== Learning objectives ===
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* Ability to draw congruent triangles
 
* Ability to draw congruent triangles
 
* Understand the properties of congruent Triangles   
 
* Understand the properties of congruent Triangles   
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=== Teaching Outlines ===
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====Concept 1: Identify congruent shapes====
 
====Concept 1: Identify congruent shapes====
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====Concept # 1. Congruent triangles ====
 
====Concept # 1. Congruent triangles ====
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===Notes for teachers===
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===Activity No # 1. Are these triangles congruent ===
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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*Estimated Time : 30 minutes.
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*Materials/ Resources needed; Laptop, projector. geogebra file and a pointer.
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*Prerequisites/Instructions, if any;
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# The students should have knowledge about triangles and its elements.
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# They should know about angles , measurements and its types.
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# They should know the meaning of the terms equal and congruent.
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# They should have a fair understanding of congruent lines and angles.
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# They should know the formulae to find area and perimeter of triangles.
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*Multimedia resources; laptop
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*Website interactives/ links/ / Geogebra Applets
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<span></span><div id="ggbContainer7bd629aa6681797b42baf608499c37c0"></div><span></span>
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*Process:
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# 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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*Developmental Questions:
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# Measure the sides and the area of both triangles.
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# Drag the points of the triangles so that you obtain two triangles with the same dimensions.
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# What are your observations about the areas of the triangles?
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# What are your observations about the perimeters of the triangles ?
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*Evaluation :
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# Define congruent triangles.
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*Question Corner:
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# List the properties of congruent triangles.
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====Concept # 2. Theorems related to congruency of triangles.====
 
====Concept # 2. Theorems related to congruency of triangles.====
 
Any triangle is defined by six measures (three sides, three angles). Triangles are congruent if:
 
Any triangle is defined by six measures (three sides, three angles). Triangles are congruent if:
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====== [[Congruence in triangles – SAS Rule]] ======
 
====== [[Congruence in triangles – SAS Rule]] ======
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===Activity No # 1. Congruency tests ===
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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: 40 minutes.
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*Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
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*Prerequisites/Instructions, if any:
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# The students should know the meaning of the terms equal and congruent.
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# They should about triangle, angles and sides.
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*Multimedia resources : Laptop
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*Website interactives/ links/ / Geogebra Applets
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This geogebra file has been taken from www.geogebratube.org – 39142. file named "Conditions for congruent triangles" Shared by ayejatt.
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<span></span><div id="ggbContainercdd96de2c194608a946e3b308ccbb61c"></div><span></span>  
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*Process:
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# The teacher can use this geogebra file to explain and clarify the "tests for congruency" by moving the sliders.
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*Developmental Questions:
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# What does congruent mean ?
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# What are congruent triangles ?
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# Name the elements of triangles ? How many are they ?
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# Do we have to know all six element measures to find if triangles are congruent ?
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# How can we find out ?
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# What are the angle measures of the two triangles ?
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# What measures are their sides ?
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# On what basis are we here knowing that the two triangles are congruent ?
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# What can this postulate be called ?
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# Recall the term postulate ?
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*Evaluation:
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# List the congruency postulates.
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# What measures are to be known to prove that given triangles are congruent ?
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*Question Corner:
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# Why SSA and AAA doesn't work ?
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====Concept # 4.Similar triangles====
 
====Concept # 4.Similar triangles====
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===Learning objectives===
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=====Learning objectives=====
 
# To develop an intuitive understanding of the concept “similarity of figures”.
 
# To develop an intuitive understanding of the concept “similarity of figures”.
 
# Triangles are similar if they have the same shape, but can be different sizes.
 
# Triangles are similar if they have the same shape, but can be different sizes.
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# To develop an ability to state and apply the definition of similar triangles.
 
# To develop an ability to state and apply the definition of similar triangles.
 
# recognize and apply “corresponding sides of similar triangles are proportional”.
 
# recognize and apply “corresponding sides of similar triangles are proportional”.
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Notes for teachers
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===Notes for teachers===
   
# The teacher can bring  different sized photographs got from same negative like stamp size, passport size and a post card size .  
 
# The teacher can bring  different sized photographs got from same negative like stamp size, passport size and a post card size .  
 
# Compare them and say that all photos are look alikes and are proportionate. only the size differs.  
 
# Compare them and say that all photos are look alikes and are proportionate. only the size differs.  
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Step 1: Find the ratio of corresponding sides in pairs of similar triangles.<br>
 
Step 1: Find the ratio of corresponding sides in pairs of similar triangles.<br>
 
Step 2: Use that ratio to find the unknown lengths.<br>  
 
Step 2: Use that ratio to find the unknown lengths.<br>  
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===Activity No # 1. SIMILAR TRIANGLES===
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======Activity No # 1. SIMILAR TRIANGLES======
 
{| 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;">
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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.”
 
# 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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===Activity No # Similarity test (AA postulate)===
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======Activity No # Similarity test (AA postulate)======
 
{| 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;">
Retrieved from "https://karnatakaeducation.org.in/KOER/en/index.php/Special:MobileDiff/30808"