# Congruence in triangles- ASA rule

From Karnataka Open Educational Resources

ASA rule: "Two triangles are congruent if two angles and an included side of one triangle are equal to two angles and an included side of another triangle."

### Objectives

- To compare given sides and angles to check for triangle congruency
- To analyse the congruency of triangles with two angles and an included side.

### Estimated time

40 minutes

### Pre-requisites/ Instructions, prior preparations

Knowledge about congruency of triangles, SAS rule of congruency of triangles, elements of congruency.

### Materials/Resources needed

Digital : Geogebra application (laptop/computer/ mobile app)

Non-digital : Paper and geometrical tools.

### Process (How to do the activity?)

Download this geogebra file from this link.

#### Procedure

- The teacher can use the Geogebra file to introduce congruency of triangles using ASA rule.
- The slider can be used to vary the measurement of side and angle of the triangles
- Bring student's attention to measurements of angles and an included side of the two trianlges.
- Verify the congruency holds good by SAS rule also(proof).

#### Developmental questions

- Observe the two triangles and identify the given elements of the triangle.
- Does the two triangles overlap on one another exactly?
- What are the elements needed to check the congruency of two triangles?
- Identify the given elements of the two triangles- 2 angles and an included side.
- Can congruency of two triangles be checked using 2 angles and an included side?
- Check the congruency of two triangles using SAS rule also and hence verify the congruency of triangles holds good by ASA rule.
- State the ASA rule for congruency of given triangles.

**Evaluation at the end of the activity**

- Can two triangles be congruent if all corresponding angles of two triangles are equal (AAA rule)?
- Draw two triangles with 2 correponding angles and an included side equal and check its congruency using ASA rule.