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 :
  1. “a. EA= Sum of opposite IAs in a triangle proof.ggb” ,
  2. “b. EA= Sum of opposite IAs in a triangle.ggb” ,
  3. “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

Triangle	Angle A	Angle B	Angle C	Exterior angle	Angle A + Angle B
Triangle1
Triangle2
Triangle3

Evaluation at the end of the activity

• Have the students able to identify the relation between  exterior and interior opposite angles of a triangle?