Difference between revisions of "Introduction to similar triangles"
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=== Objectives === | === Objectives === | ||
− | + | *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. | |
− | + | *Understand that 'corresponding' means matching and 'congruent' means equal in measure. | |
− | + | *To determine the correspondences between the pairs of similar triangles. | |
− | + | *The ratio of the corresponding sides is called the ratio of similitude or scale factor. | |
− | + | *Triangles are similar if their corresponding angles are congruent and the ratio of their corresponding sides are in proportion. | |
− | + | *To develop an ability to state and apply the definition of similar triangles. | |
− | + | *recognize and apply “corresponding sides of similar triangles are proportional”. | |
===Estimated Time=== | ===Estimated Time=== | ||
+ | 45 minutes. | ||
=== Prerequisites/Instructions, prior preparations, if any === | === Prerequisites/Instructions, prior preparations, 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. | ||
===Materials/ Resources needed=== | ===Materials/ Resources needed=== | ||
− | + | Digital resources: Laptop, geogebra file, projector and a pointer. | |
− | |||
− | + | Geogebra file: | |
− | What are the | + | ===Process (How to do the activity)=== |
− | + | #The teacher can use this geogebra file to explain about similar triangles. | |
− | + | #Also she can help differentiate between congruent and similar triangles. | |
+ | *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. | ||
− | + | Notes for teachers | |
+ | #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 are equal or corresponding sides are 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 : |
Revision as of 09:18, 29 April 2019
Objectives
- 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.
- Understand that 'corresponding' means matching and 'congruent' means equal in measure.
- To determine the correspondences between the pairs of similar triangles.
- The ratio of the corresponding sides is called the ratio of similitude or scale factor.
- Triangles are similar if their corresponding angles are congruent and the ratio of their corresponding sides are in proportion.
- To develop an ability to state and apply the definition of similar triangles.
- recognize and apply “corresponding sides of similar triangles are proportional”.
Estimated Time
45 minutes.
Prerequisites/Instructions, prior preparations, 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.
Materials/ Resources needed
Digital resources: Laptop, geogebra file, projector and a pointer.
Geogebra file:
Process (How to do the activity)
- The teacher can use this geogebra file to explain about similar triangles.
- Also she can help differentiate between congruent and similar triangles.
- 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.
Notes for teachers
- 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 are equal or corresponding sides are 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 :