Relation between interior and exterior angles in triangle

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Interior angle and the corresponding angle form a linear pair. This exterior angle in relation to the remote interior angles and their dependencies are deducted with the theorem.

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


Download this geogebra file from this link.


Download this geogebra file from this link.


Download this geogebra file from this link.


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?