Difference between revisions of "Similar and congruent triangles"

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= Teaching Outlines =
 
= Teaching Outlines =
  
−
==Concept #1. What are similar triangles ? Their characteristics.==
+
==Concept #1. What are similar triangles ? ==
 
===Learning objectives===
 
===Learning objectives===
 
===Notes for teachers===
 
===Notes for teachers===
−
===Activity No # ===
+
===Activity No # 1 SIMILAR TRIANGLES===
 
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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>
 
|}
 
|}
−
*Estimated Time
+
*Estimated Time:45 minutes.
−
*Materials/ Resources needed
+
*Materials/ Resources needed:
−
*Prerequisites/Instructions, if any
+
Laptop, geogebra file, projector and a pointer.
−
*Multimedia resources
+
*Prerequisites/Instructions, if any:
 +
# The students should have prior knowledge of triangles , sides , angles , vertices .
 +
# They should know meaning of the terms 'similar' and 'proportionate'.
 +
# They should be able to identify  the corresponding sides.
 +
# They should know how to find ratio.
 +
# They should know to find area and perimeter of triangles.
 +
# The students should have clarity between the terms congruent and similar.
 +
*Multimedia resources: Laptop
 
*Website interactives/ links/ / Geogebra Applets
 
*Website interactives/ links/ / Geogebra Applets
−
*Process/ Developmental Questions
+
*Process:
−
*Evaluation
+
# 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.
−
*Question Corner
+
# She can also mention about scale concept in graphical representation.
 +
# Hence similar triangles are the same proportionate triangles but of different sizes.
 +
# Two triangles are similar  if they have:
 +
* all their angles equal
 +
* corresponding sides in the same ratio
 +
# In similar triangles, the sides facing the equal angles are always in the same ratio.
 +
# Application of this finds its use in finding  the unknown lengths in similar triangles . For this :
 +
Step 1: Find the ratio of corresponding sides in pairs of similar triangles.
 +
Step 2: Use that ratio to find the unknown lengths.
 +
*Developmental Questions:
 +
# Look at the shape of both triangles being formed? (look alikes )
 +
# As I increase /decrease the size of triangles do you see that the measures are changing proportionately ?
 +
# Can any one explain what exactly  proportionately means ?
 +
# Can you identify the corresponding sides and angles ?
 +
*Evaluation:
 +
# Name the corresponding sides.
 +
# Compare the perimeters of two similar triangles.
 +
# What are equiangular triangles ?
 +
*Question Corner:
 +
# Compare the ratio of corresponding sides of similar triangles. What do you infer ?
 +
# How can one draw similar triangles if only one triangles sides are given ?
 +
# Discuss the applications of similar triangles in finding unknowns in real life situations.
 +
# Give examples where one uses the concept of similarity.
  
 
===Activity No # ===
 
===Activity No # ===

Revision as of 16:36, 2 November 2013

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

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Teaching Outlines

Concept #1. What are similar triangles ?

Learning objectives

Notes for teachers

Activity No # 1 SIMILAR TRIANGLES

  • Estimated Time:45 minutes.
  • Materials/ Resources needed:

Laptop, geogebra file, projector and a pointer.

  • Prerequisites/Instructions, if any:
  1. The students should have prior knowledge of triangles , sides , angles , vertices .
  2. They should know meaning of the terms 'similar' and 'proportionate'.
  3. They should be able to identify the corresponding sides.
  4. They should know how to find ratio.
  5. They should know to find area and perimeter of triangles.
  6. The students should have clarity between the terms congruent and similar.
  • Multimedia resources: Laptop
  • Website interactives/ links/ / Geogebra Applets
  • Process:
  1. 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.
  2. She can also mention about scale concept in graphical representation.
  3. Hence similar triangles are the same proportionate triangles but of different sizes.
  4. Two triangles are similar if they have:
  • all their angles equal
  • corresponding sides in the same ratio
  1. In similar triangles, the sides facing the equal angles are always in the same ratio.
  2. Application of this finds its use in finding the unknown lengths in similar triangles . For this :

Step 1: Find the ratio of corresponding sides in pairs of similar triangles. Step 2: Use that ratio to find the unknown lengths.

  • Developmental Questions:
  1. Look at the shape of both triangles being formed? (look alikes )
  2. As I increase /decrease the size of triangles do you see that the measures are changing proportionately ?
  3. Can any one explain what exactly proportionately means ?
  4. Can you identify the corresponding sides and angles ?
  • Evaluation:
  1. Name the corresponding sides.
  2. Compare the perimeters of two similar triangles.
  3. What are equiangular triangles ?
  • Question Corner:
  1. Compare the ratio of corresponding sides of similar triangles. What do you infer ?
  2. How can one draw similar triangles if only one triangles sides are given ?
  3. Discuss the applications of similar triangles in finding unknowns in real life situations.
  4. Give examples where one uses the concept of similarity.

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 #2. Similarity postulates

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. Theorems on similar triangles

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

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 #1. What are congruent triangles ? Their characteristics.

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 #2. Congruency postulates

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. Theorems on congruent triangles

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

Activity No #

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




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