Sum of the interior angles of a quadrilateral
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°
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|
- 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||
|Sum of angles||Angle 1||Angle 2||
|Sum of angles|
Evaluation at the end of the activity
- Is the sum of all angles in any quadrilateral 360o.