Congruence in triangles- ASA rule

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.

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?)

Procedure

1. The teacher can use the Geogebra file to introduce congruency of triangles using ASA rule.
2. The slider can be used to vary the measurement of side and angle of the triangles
3. Bring student's attention to measurements of angles and an included side of the two trianlges.
4. 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.