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.

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.

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.