# Similarity test - AA postulate

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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

- The students should know the meaning of the terms congruent and similar.
- They should understand the terms corresponding sides and angles.
- They should have an idea of ratio and proportion.

### Materials/ Resources needed

- Digital : Computer, geogebra application, projector.
- Non digital : Worksheet and pencil.
- Geogebra file:

### Process (How to do the activity)

- The teacher can initially have a warm up session regarding terms congruence, similarity and corresponding angles and ratio.
- 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.
- Also she can let them understand that in similar triangles, the corresponding sides are proportional.

- Developmental Questions:

- What does congruent mean ?
- What does similarity mean ?
- How can we test whether the two given figures are similar or not ?
- In the above two triangles, what measures of both are same ?
- Identify the corresponding sides and angles.
- Is their ratio same ?
- What can you say about the two triangles ?
- Recall the similarity postulates.
- By what postulate are the two triangles similar ?

- Evaluation:

- Differentiate similarity and congruence.

- Question Corner:

- Can the tree and its shadow be considered as similar figures ?
- 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.