Sum of the interior angles of a quadrilateral

The sum of the measures of the angles in any quadrilateral is 4 right angles.

Objectives

To establish that sum of interior angles of any quadrilateral is 360°

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’

Download this geogebra file from this link.

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

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 

Observation	Triangle1				Triangle2				Sum of angles of two triangle
	Angle 1	Angle 2	Angle 3	Sum of angles	Angle 1	Angle 2	Angle 3	Sum of angles
Q1
Q2
Q3

Evaluation at the end of the activity

• Is the sum of all angles in any quadrilateral 360^o.