Sum of the interior angles of a quadrilateral

Objectives

1. To establish that sum of interior angles of any quadrilateral is 360^o

Estimated Time

40 minutes

Prerequisites/Instructions, prior preparations, if any

Prior knowledge of point, lines, angles, intersecting lines, vertically opposite angles, properties of triangle

Materials/ Resources needed

• Digital: Computer, geogebra application, projector.
• Non digital : Worksheet and pencil
• Geogebra files : ‘Sum of the interior angles of a quadrilateral.ggb’

Process (How to do the activity)

• In the geogebra sketch for the quadrilateral measure the sides and angles at the vertices
• Calculate the sum of these angles of the quadrilateral? Note your observations
• {| class="wikitable" |Quadrilateral |Side1 |Side2 |Side3 |Side4 |Angle1 |Angle2 |Angle3 |Angle4 |Angle1+Angle 2+ Angle3 + Angle 4 |Whatdo you observe about their sum |- |Q1 | | | | | | | | | | |- |Q2 | | | | | | | | | | |- |Q3 | | | | | | | | | | |}

• Draw any one diagonal. What do you notice? What is the quadrilateral divided into? How many triangles are formed?
• What is the measure of the sum of angles in each quadrilateral? So what is the measure of all the angles of the quadrilateral?
• Make different quadrilaterals. Divide it into two triangles, measure the angles of the two triangles, check their sum.
• Tabulate the angles of the two triangles  {| class="wikitable" |Observation | colspan="4" |Triangle1 | colspan="4" |Triangle2 |Sum of angles of two triangle Triangle1 + Triangle2 |- | |Angle 1 |Angle 2 | Angle 3 |Sum of angles |Angle 1 |Angle 2 | Angle 3 |Sum of angles | |- |Q1 | | | | | | | | | |- |Q2 | | | | | | | | | |- |Q3 | | | | | | | | | |}