ACTIVITY OBJECTIVE

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

MATERIAL REQUIRED

Chart paper, geometry box. scissors, sketch pens, adhesive, transparent sheet.

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. tve repuy she

Fi R^ - 1

Fig. 2

Fig, 3

no

DEMONSTRATION

Paste cut-outs of the opposite angles 21 and angle3 angle2 and 24 to make straight angles as shown in Fig . Thus angle1+ angle3=180^ and angle2+ angle4=180^ .

OBSERVATION

On actual measurement:

angle1=.. . angle2=. .

angle3=.; angle4=.

angle2+ angle4=.:

So, angle1+ angle3=.;

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

APPLICATION

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

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

MATERIAL REQUIRED

Chart paper, geometry box. scissors, sketch pens, adhesive, transparent sheet.

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. tve repuy she

Fi R^ - 1

Fig. 2

Fig, 3

no

DEMONSTRATION

Paste cut-outs of the opposite angles 21 and angle3 angle2 and 24 to make straight angles as shown in Fig . Thus angle1+ angle3=180^ and angle2+ angle4=180^ .

OBSERVATION

On actual measurement:

angle1=.. angle2=.

angle3=; angle4=

angle2+ angle4=:

So, angle1+ angle3=;

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

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: