Similar and congruent triangles

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= Concept Map =

similar_and_congruent_triangles.mm

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=Additional Information=

Reference Books
= Teaching Outlines =

Learning objectives

 * 1) The students need to develop an intuitive understanding of the concept “similarity of figures”.
 * 2) The students need understand that 'corresponding' means matching and 'congruent' means equal in measure.
 * 3) They should be able to determine the correspondences between the pairs of similar triangles.
 * 4) The ratio of the corresponding sides is called the ratio of simultude or scale factor.
 * 5) In mathematics, polygons are similar if their corresponding  angles are congruent and the ratio of their corresponding sides are in proportion.
 * 6) They should be able to state and apply the definition of similar polygons.
 * 7) recognize and apply “corresponding sides of similar triangles are proportional”.

Activity No # 1 SIMILAR TRIANGLES
Laptop, geogebra file, projector and a pointer. Step 1: Find the ratio of corresponding sides in pairs of similar triangles. Step 2: Use that ratio to find the unknown lengths.
 * Estimated Time:45 minutes.
 * Materials/ Resources needed:
 * Prerequisites/Instructions, 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.
 * 6) The students should have clarity between the terms congruent and similar.
 * Multimedia resources: Laptop
 * Website interactives/ links/ / Geogebra Applets
 * Process:
 * 1) 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.
 * 2) She can also mention about scale concept in graphical representation.
 * 3) Hence similar triangles are the same proportionate triangles but of different sizes.
 * 4) Two triangles are similar  if they have:
 * all their angles equal
 * corresponding sides in the same ratio
 * 1) In similar triangles, the sides facing the equal angles are always in the same ratio.
 * 2) Application of this finds its use in finding  the unknown lengths in similar triangles . For this :
 * 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.

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