AMSCO'S Geometry. New York - Rye High School

416 QuadrilateralsExplorationIn Chapter 5 we found that the perpendicular bisectors of the sides of a triangleintersect in a point called the circumcenter. Do quadrilaterals also have circumcenters?In this activity, you will explore the perpendicular bisectors of the sidesof quadrilaterals. You may use compass and straightedge or geometrysoftware.a. Construct the perpendicular bisectors of two adjacent sides of each of thefollowing quadrilaterals.b. Construct the third and fourth perpendicular bisectors of the sides of eachof the quadrilaterals. For which of the above quadrilaterals is the intersectionof the first two perpendicular bisectors the same point as the intersectionof the last two perpendicular bisectors?c. When all four perpendicular bisectors of a quadrilateral intersect in thesame point, that point is called the circumcenter. Of the specific quadrilateralsstudied in this chapter, which types do you expect to have a circumcenterand which types do you expect not to have a circumcenter?d. For each of the quadrilaterals above that has a circumcenter, place thepoint of your compass on the circumcenter and the pencil on any of thevertices. Draw a circle.e. Each circle drawn in d is called the circumcircle of the polygon. Based onyour observations, write a definition of circumcircle.