1. Note 7: Cyclic Quadrilaterals

2. 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.

3. 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

4. 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

5. Which of these shapes is cyclic? A is not cyclic. Opposite angles do not add to 180 o B is cyclic because 131 + 49 = 180 o

6. Page 212 Exercise J