Construction of a triangle with two angles and included side

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Construction of a triangle when two angles of a triangle and a side are known and understanding the side given can only be constructed between the two angles to form a unique triangle. Construction follows ASA congruence rule.

Objectives

• To construct a triangle given two sides and an angles
• To understand the given angle should be included angle when two sides are given

20 minutes

Prerequisites/Instructions, prior preparations, if any

Prior understanding of point, lines and angles, elements of triangle, properties of triangle

Materials/ Resources needed

Download this geogebra file from this link.

Process (How to do the activity)

• For given 2 angles, if the angles add to 180o, can you construct the triangle?
• Is it possible to construct a triangle with only 2 given angles. What is the other parameter required for construction.
• If any one side is specified, along with 2 angles how many triangles are possible.
• If the side given is an included side, how many triangles are possible.

Evaluation at the end of the activity

• Why should the given side be included side?
• For the given A, A and S are the triangles AAS,  ASA and SAA congruent triangles.