# Introduction to similar triangles

From Karnataka Open Educational Resources

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

- 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 : 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)

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