Page 69 - Mathematics Class - IX

INFERENCE
The opposite angles of a cyclic quadrilateral are always supplementary.

EXTENDED TASK
1. Using paper folding method, find out whether the two properties are true for a non-cyclic quadrilateral or not.

2. Take any four points on the circles of different radii and join them to form a quadrilateral. What do you
observe?

APPLICATION

This property can be used in solving various problems in geometry.

Viva-Voce

1. Define a cyclic quadrilateral.
Ans. A cyclic quadrilateral is a quadrilateral which has all its vertices lying on a circle.

2. State any two properties of a cyclic quadrilateral.
Ans. (i) The sum of either pair of opposite angles is 180°.
(ii) The exterior angle is equal to opposite interior angle.

3. Which axiom is used to prove that the exterior angle of a cyclic quadrilateral is equal to the interior opposite
angles?
Ans. Linear pair axiom.

4. What is a non-cyclic quadrilateral?
Ans. A quadrilateral in which the sum of opposite angles is not supplementary.
5. In figure, find ∠1, ∠2 and ∠3.

Ans. ∠1 = 110°, ∠2 = 115°, ∠3 = 110°

70° 65°
1

2 3

6. ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and
∠ECD = 35° then what is the measure of ∠BAC?
Ans. 103°

67