Relation between interior and exterior angles in triangle

An exterior angle of the triangle is the angle between one side of a triangle and the extension of an adjacent side. Exterior angle of the triangle has a relation with interiors of the triangle.

Objectives
To show interior angles of a triangle have a relation with its exterior angles.

Estimated Time
40 minutes

Prerequisites/Instructions, prior preparations, if any
Prior understanding of point, lines and angles, adjacent angles, vertically opposite angles, linear pair

Materials/ Resources needed

 * Digital : Computer, geogebra application, projector.
 * Non digital : Worksheet and pencil.
 * Geogebra files :
 * “a. EA= Sum of opposite IAs in a triangle proof.ggb” ,
 * “b. EA= Sum of opposite IAs in a triangle.ggb” ,
 * “c. EA= Sum of opposite IAs in a triangle demo.ggb”

Process (How to do the activity)

 * In the triangle students should identify the angles of the triangle.
 * Extend one side, students should recognize the exterior angle formed.
 * What is the sum of the angles of a triangle?
 * Students should be able to recognize the alternate angle formed for one of the interior angle(Angle BAC)
 * Drag the parallel line to the opposite vertex, to place the alternate angle next to the angle at the opposite vertex.
 * Compare the angles formed and the exterior angle, do they have a relation.
 * How are the two angles together related to the exterior angle?
 * Do you notice any relation between the exterior angle and the interior angles
 * If you know the measure of interior angle can you find the corresponding exterior angle?
 * The other two files can be used to demonstrate the the relation between the exterior angle and opposite interior angles.
 * Note the measure of angles

Evaluation at the end of the activity
 * Have the students able to identify the relation between  exterior and interior opposite angles of a triangle?