Note 7: Cyclic Quadrilaterals. A cyclic quadrilateral has all four vertices on a circle. (concyclic points) Opposite angles of a cyclic quadrilateral.

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Presentation transcript:

Note 7: Cyclic Quadrilaterals

A cyclic quadrilateral has all four vertices on a circle. (concyclic points) Opposite angles of a cyclic quadrilateral add to 180 o The exterior angle of a cyclic quadrilateral equals the opposite interior angle.

Example 1 Find angle A with a geometrical reason. A 47 o A = 180 – 47 = 133 o Opposite angles of a cyclic quad add to 180º

Example 2: Find, with geometrical reasons the unknown angles. 105 o C D 41 o C = 41 o D = 180 – 105 = 75 o Exterior angle of a cyclic quad equals the opposite interior angle Opposite angles in a cyclic quad add to 180º

Which of these shapes is cyclic? A is not cyclic. Opposite angles do not add to 180 o B is cyclic because = 180 o

Page 212 Exercise J