Class 09 To verify that the opposite angles of a cyclic quadrilateral are supplementary.

 

Activity 24

OBJECTIVE	MATERIAL REQUIRED
To verify that the opposite angles of a	Chart  paper,  geometry  box,scissors, sketch pens, adhesive, transparent sheet.

 cyclic quadrilateral are supplementary.

 METHOD OF CONSTRUCTION

 1.   Take a chart paper and draw a circle of radius on it.

 2.    In the circle, draw a quadrilateral so that all the four vertices of the quadrilateral lie on the circle. Name the angles and colour them as shown in Fig. 1.

 3.   Make the cut-outs of the angles as shown in Fig. 2.

DEMONSTRATION

Paste cut-outs of the opposite angles ∠1 and ∠3, ∠2 and ∠4 to make straight angles as shown in Fig. 3. Thus ∠1 + ∠3 = 180° and ∠2 + ∠4 = 180°.

OBSERVATION

On actual measurement:

∠1 = ................;    ∠2 = ................;          ∠3 = ................;      ∠4 = ................. 

So, ∠1 + ∠3 = ..........;              ∠2 + ∠4 = ..........; 

Therefore, sum of each pair of the opposite angles of a cyclic quadrilateral is

 ........................ 

       APPLICATION 

The concept may be used in solving various problems in geometry.