Inscribed Polygons

Students should be familiar with basic shapes such as triangles and circles, as well as trigonometric concepts such as perpendicular bisectors. Other concepts needed are midpoint and distance equations, Pythagorean theorem, and slope of a line.

Working in groups of two, students complete an exploration activity to determine whether a circle can be drawn through the vertices of any triangle. The students will take notes on the theory of inscribed triangles and then participate in a guided example on the board/overhead. Students then work on problems to reinforce these concepts.

Students will be able to
1. understand that it is always possible to circumscribe a circle about a triangle
2. identify chords of a circle
3. identify that the perpendicular bisector of a chord of a circle passes through the center of a circle
4. apply these concepts to problems

Rulers, compasses

Mathematics

Grade 10
Geometry and Spatial Sense

C. Recognize and apply angle relationships in situation involving intersecting lines,
perpendicular lines and parallel
D. Use coordinate geometry to represent and examine the properties of geometric figures
E. Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass, and technology
G. Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.

Mathematical Processes

A. Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution
B. Apply mathematical knowledge and skills routinely in other content areas and practical situations.
computerized microscopes).