Introduction to similar triangles

Concept of similarity is introduced and investigated by comparing elements of two triangles.

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

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.

Materials/ Resources needed

• Digital : Computer, geogebra application, projector.
• Non digital : Worksheet and pencil.
• Geogebra file: Demo of similar triangles.ggb ,Similar triangle 1.ggb, Similar triangle 2 ratio.ggb, Similar triangle 3 ratio.ggb
  

Download this geogebra file from this link.

Download this geogebra file from this link.

Download this geogebra file from this link.

Download this geogebra file from this link.

Process (How to do the activity)

1. The teacher can use this geogebra file to explain about similar triangles.
2. Also she can help differentiate between congruent and similar triangles.

• 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.

Notes for teachers

1. The teacher can bring different sized photographs got from same negative like stamp size, passport size and a post card size .
2. Compare them and say that all photos are look alikes and are proportionate. only the size differs.
3. She can also mention about scale concept in graphical representation.
4. Hence similar triangles are the same proportionate triangles but of different sizes.
5. Two triangles are similar if they have: all their angles are equal or corresponding sides are in the same ratio
6. 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 :
   1. Step #1: Find the ratio of corresponding sides in pairs of similar triangles.
   2. Step #2: Use that ratio to find the unknown lengths.