Cyclic Quadrilateral Property

Objective

To verify that opposite angles of a cyclic quadrilateral are supplementary.

Theory

1. What is a Quadrilateral?

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.

Following are examples of a quadrilateral.

                                             

                                                                  Fig. (A) Polygon

2. Cyclic Quadrilateral  -

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also called an inscribed quadrilateral.

                                                            

                                                           Fig. (B) Cyclic Quadrilateral

3. Supplementary angles - 

Supplementary angles are those angles that sum up to 180°. For example, angle 120° and angle 60° are supplementary angles because the sum of 120° and 60° is equal to 180°.

 

                                                       

                                                     Fig. (C) Supplementary Angles