Page 67 - Mathematics Class - IX

ACTIVITY 4.8

OBJECTIVE

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

MATERIALS REQUIRED
Cardboard Scissors
White paper Sketch pens

Drawing sheet Adhesive
Geometry box Transparent sheet

PRE-REQUISITE KNOWLEDGE

1. Concept of supplementary angles, linear pair axiom and interior opposite angles.
2. Basic information of cyclic quadrilateral.

THEORY
1. Supplementary angles: Two angles are said to be supplementary, if the sum of their measures is 180º.

2. If a ray stands on a line, then the sum of two adjacent angles so formed is 180º, i.e. the sum of the linear
pair is 180º.
In the given Fig. (a), ∠AOC + ∠BOC = 180º.
If the sum of two adjacent angles is 180º, then the non-common arms of the angles form a line or two
opposite rays. The two axioms given together are called the linear pair axiom.

C

O
A B
Fig. (a)

3. Cyclic quadrilateral: A quadrilateral ABCD is cyclic if all the four vertices A, B, C and D are concyclic,
i.e. A, B, C, and D lie on a circle.
A

B

D

C
Fig. (b): Cyclic quadrilateral
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