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Euclidean and non-Euclidean Geometry – Fall 2008 Dr. Hamblin Final Project: Cyclic Quadrilaterals In this project, you will investigate cyclic quadrilaterals. Definition: A cyclic quadrilateral is a quadrilateral whose vertices all lie on a circle. In your presentation, you will investigate these conjectures. You should investigate whether or not the statements are true or false using Sketchpad. If the statement is true, you should attempt to prove it. If the statement is false, then you should show a counterexample. Conjecture #1: If a quadrilateral is cyclic, then its opposite angles are supplementary. Conjecture #2: The perpendicular bisectors of the four sides of a cyclic quadrilateral all intersect at the center of the circle. Conjecture #3: If a quadrilateral has opposite angles supplementary, then it is cyclic. Generalizations/Extensions Investigate cyclic pentagons, cyclic hexagons, etc. Try to make similar conjectures about these shapes. Can you prove your conjectures?
