Interior and exterior angles in triangle

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Objectives

  • Identify all angles when a triangle is formed
  • Understand the relation between various angles that are formed in a triangle.

Estimated Time

Prerequisites/Instructions, prior preparations, if any

Prior knowledge of point, lines, angles

Materials/ Resources needed

  • Digital : Computer, geogebra application, projector.
  • Non digital : Worksheet and pencil.
  • Geogebra files : Angles of triangle.ggb

Process (How to do the activity)

  • Ask students how many lines are there? They should be able to identify the points of intersection of the lines. How many points of intersection are formed?
  • How many angles are formed at an intersecting point? How many angles in total at the three points of intersection?What is the total angle measure at each intersecting point?
  • How many angles are inside the triangle and how many are outside the triangle
  • Can you find an exterior angle that is equal to the interior angle of a triangle at each vertex?Why are they equal?
  • Identify the exterior angles that are equal? Justify why they are equal.
  • Establish that there are 2 angles which are exterior of the triangle that are equal and are formed when the sides of the triangle is extended at the vertex.
  • Students to analyze the interior and exterior angle at each point to find a relation between the interior angle and one of the exterior angles at the vertex. Students should be able to recognize the linear pair formed by interior angle and exterior angle.
  • Vary the position of the lines to check if interior and exterior angles form a linear pair.
  • Note the measure of angles
Angles of the triangle Exterior angle Interior angle + Exterior angle
Angle 1 Angle 2 Angle 3 Angle 1 Angle 2 Angle 3 In Angle 1

+

Ex Angle1

In Angle 2

+

Ex Angle2

In Angle 3

+

Ex Angle3

Evaluation at the end of the activity

  • Are students able to recognize interior and exterior angles in a triangle
  • Have the students able to find a relation between the interior angle and exterior angle that are formed at each vertex?