Congruence in triangles – SAS Rule

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Given two sides and an angle of two triangles are equal, are the two triangles congruent? This activity investigates the position of the given angle for the two triangles to be congruent. 

Objectives

  • Compare given sides and angles to check for triangle congruency
  • Understand the angle given should be included angle

Estimated Time

30 minutes

Prerequisites/Instructions, prior preparations, if any

Prior knowledge of point, lines, angles, elements of triangle, close figures

Materials/ Resources needed

  • Digital : Computer, geogebra application, projector.
  • Non digital : Worksheet and pencil.
  • Geogebra files : “SAS congruency.ggb


Download this geogebra file from this link.


Process (How to do the activity)

  • If one side is fixed and an angle is fixed will the two triangles be congruent?
  • How many triangles can be possible for a given side and a given angle?
  • What is the other parameter that needs to be fixed?
  • If two sides are congruent in two triangles will the triangles be congruent.
  • Do you need another parameter for the two triangles to be congruent. What other parameter is required - Angle / Side
  • If another side is fixed – which rule of congruency does it become?
  • Which other angle is required to be fixed for the two triangles to be congruent?
  • HW : Construct two triangles with one side and one angle same. Check if they are

Evaluation at the end of the activity

  • Students should understand if two sides are given the angle should be included for the triangles to be congruent.
  • Students should be able to compare the parameters given to check for congruence