Cyclic quadrilateral Class IX Prepared by P.E.Venugopalan K.V.KELTRON NAGAR.

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Presentation transcript:

Cyclic quadrilateral Class IX Prepared by P.E.Venugopalan K.V.KELTRON NAGAR

Cyclic quadrilateral  A quadrilateral is called a cyclic quadrilateral if all the four vertices of it lie on a circle

Theorem (10.11)  The sum of either pair of opposite angles of a cyclic quadrilateral is 180° D C B A If ABCD is a cyclic quadrilateral,then (i) ∟A + ∟C =180° and (ii) ∟B + ∟D = 180°

Converse of Theorem  If the sum of a pair of opposite angles of a quadrilateral is 180°,the quadrilateral is cyclic(Theorem 10.12) A D C B ABCD is a cyclic quadrilateral if (i) ∟A + ∟C =180° Or (ii) ∟B + ∟D = 180°