Sum of the interior angles of a quadrilateral

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


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

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
  • 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

Evaluation at the end of the activity

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