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

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