Page 68 - Mathematics Class - IX

PROCEDURE

1. Take a cardboard and using adhesive, paste a white paper on it. A

2. Draw a circle and paste it on cardboard. B
3. In the circle, draw a quadrilateral ABCD such that all the four vertices
of quadrilateral lie on the circle. Name the angles as ∠A, ∠B, ∠C and C
∠D (Fig. (c)). D

Fig. (c)

4. Make the cut outs of the angles, (i.e. ∠A, ∠B, ∠C and ∠D) with the help of a transparent sheet (Fig. (d)).

A
B
C
D

Fig. (d)

5. By using adhesive, paste cut outs of the opposite angles ∠A and ∠C; ∠B and ∠D. (Fig. (e)).

C B
A D

Fig. (e)

6. Joining the opposite angles ∠A and ∠C, ∠B and ∠D, we get straight angles (Fig. (e)). Hence,
∠A + ∠C = 180º and ∠B + ∠D = 180º.

OBSERVATIONS

By actual measurement,

∠A = ................, ∠B = ..............,

∠C = ................, ∠D = ..............,

So, ∠A + ∠C = .......... ∠B + ∠D = ......... .

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

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