Sum of angles at point of intersection of diagonals in a quadrilateral

A diagonal is the line segment that joins a vertex of a polygon to any of its non-adjacent vertices. This two diagonals of a quadrilateral form angle, this activity explores property of these angles.

Objectives

To understand sum of angles at the point of intersection of diagonal of a quadrilateral is 360°.

Estimated Time

30 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 angles at point of intersection of diagonals in a quadrilateral.ggb

Download this geogebra file from this link.

Process (How to do the activity)

1. Explore various parameters of a quadrilateral – length of line segments making a quadrilateral, angles of a quadrilateral, length of diagonals

2. How are the two diagoanls of a quadrilateral

3. How many angles are formed at point of intersection of these diagonals

4. How many angles are equal, what are they called

5. What is the sum of angles of around two intersecting lines

• Evaluation at the end of the activity

1. Is the above property true for any quadrilateral