Ultimately, the instructor should focus students on the fact that, for apolygon to be inscribed in a circle all vertices of the polygon must lie on thesame circle. The instructor maychoose to focus on previous work with inscribed triangles or may extend thediscussion to other contexts. Theinstructor will begin the lesson by reviewing the concept of inscribedpolygons. StudentData Organization Table (optional).DynamicSketch.gspGeometer’s Sketchpad file.After articulating theirfindings, students will use formal proof to confirm their conjectures. Students will then analyze their data to form conjectures about whatquadrilateral properties determine whether a quadrilateral can be inscribed ina circle. Students can examine andcollect data about the properties associated with irregular quadrilaterals thatcan be inscribed in a circle. Students will then expand their search of quadrilateralsthat can be inscribed in a circle by manipulating the Geometer’s Sketchpad fileprovided. Students will collect data about theproperties of each of these quadrilaterals. UsingGeometer’s Sketchpad software, students will construct familiar quadrilateralsand determine whether each can be inscribed in a circle.
Studentswill analyze data, determining the properties that determine whether aquadrilateral can be inscribed in a circle.Studentswill organize data using either a chart or electronic spreadsheet.Studentswill note whether particular quadrilaterals can be inscribed in a circle andrecord properties of these quadrilaterals, such as angle measures and sidelengths.Studentscreate numerous quadrilaterals including the following and determine if theycan be inscribed in a circle: square, rectangle, parallelogram, rhombus, trapezoid, kite, irregularquadrilateral.
Completing the activities in this lesson is anticipated torequire 1.5 one-hour class periods. This lesson is designed for implementation with highschool students studying Euclidean Geometry.
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