Ask students to begin with a triangle, then a quadrilateral, a pentagon, a hexagon, and so forth. By collecting and organizing this information, students should see a pattern emerge and can write a generalization for the sum of the interior angles of an n-sided polygon. The student analyzes properties and describes relationships in geometric figures. Based on explorations and using concrete models, the student formulates and tests conjectures about the properties and attributes of circles and the lines that intersect them. Clarifying Activity Using construction technology or a circular geoboard, students construct a circle.
Students select points A and B on the circle and construct a secant line.
Students find the measure of the angle formed by the secant and the radius to point A. Students use the technology, or the rubber bands on the geoboard, to move point B until it coincides with point A creating a tangent line. For any point on a circle, the tangent and radius that contains the point of tangency are perpendicular. The student analyzes properties and describes relationships in geometric figures. The student analyzes the characteristics of three-dimensional figures and their component parts. Clarifying Activity Students investigate the questions below to analyze the design of juice boxes and their straws.