Similarity test - AA postulate

In two triangles, if the angles are equal, then the sides opposite to the equal angles are in the same ratio and hence the two triangles are similar.

Objectives
To understand two triangles are similar if any two angles of the triangles are congruent.

Estimated Time
45 minutes

Prerequisites/Instructions, prior preparations, if any

 * 1) The students should know the meaning of the terms congruent and similar.
 * 2) They should understand the terms corresponding sides and angles.
 * 3) They should have an idea of ratio and proportion.

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 initially have a warm up session regarding terms congruence, similarity and corresponding angles and ratio.
 * 2) She can then project the geogebra file and by moving the sliders she can change the side and angle measures and teach teh AA similarity postulate.
 * 3) Also she can let them understand that in similar triangles, the corresponding sides are proportional.
 * Developmental Questions:
 * 1) What does congruent mean ?
 * 2) What does similarity mean ?
 * 3) How can we test whether the two given figures are similar or not ?
 * 4) In the above two triangles, what measures of both are same ?
 * 5) Identify the corresponding sides and angles.
 * 6) Is their ratio same ?
 * 7) What can you say about the two triangles ?
 * 8) Recall the similarity postulates.
 * 9) By what postulate are the two triangles similar ?
 * Evaluation:
 * 1) Differentiate similarity and congruence.
 * Question Corner:
 * 1) Can the tree and its shadow be considered as similar figures ?
 * 2) Can this similarity concept be used to find the height and depth of objects ? Frame any two of your own questions which can be solved using similarity postulates.