Difference between revisions of "Similar and congruent triangles"
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Revision as of 10:34, 20 November 2013
| Philosophy of Mathematics |
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Teaching Outlines
Concept #1.Similar triangles and similarity postulates
Learning objectives
- The students need to develop an intuitive understanding of the concept “similarity of figures”.
- The students need understand that 'corresponding' means matching and 'congruent' means equal in measure.
- They should be able to determine the correspondences between the pairs of similar triangles.
- The ratio of the corresponding sides is called the ratio of simultude or scale factor.
- In mathematics, polygons are similar if their corresponding angles are congruent and the ratio of their corresponding sides are in proportion.
- They should be able to state and apply the definition of similar polygons.
- recognize and apply “corresponding sides of similar triangles are proportional”.
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:
- 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
- Process:
- 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.
- 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 #
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Concept #2. 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
Concept # 3. Congruent triangles and test for congruency
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 # 4. 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
Concept #
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
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