1. Geometry: From Triangles to Quadrilaterals and Polygons

2. MA.912.G.2.2 Determine the measures of interior and exterior angles of polygons, justifying the method used Block 23

3. Introduction Definitions: Angle: Two rays or two line segments extending from a common end point called a vertex. Angles are measured in degrees, in radians, or in gradians. Interior angle Central angle

4. Interior, exterior and central angles Definitions

5. Interior, exterior and central angles Interior angles: The angles on the inside of a polygon formed by each pair of adjacent sides.

6. Interior, exterior and central angles Exterior angle: the angle formed by any side of a polygon and the extension of its adjacent side

7. Interior, exterior and central angles Central angle: The angle subtended at the center of the polygon by one of it's sides. We will be interested only in central angles for regular polygons:

8. Properties of central angles If a regular polygon is inscribed in a circle (that is, drawn so that its vertices lie on the circumference of the circle), then the central angles formed when rays are drawn from the center of the circle to the vertices are congruent.

9. Properties of central angles For example, the regular pentagon is inscribed in a circle, and a ray has been drawn from the center to each vertex. These rays divide the equilateral triangle into 5 congruent isosceles triangles, and the 5 central angles are congruent.

10. Class activity: This lesson we investigate reflections using hinged mirrors. With a kaleidoscope, we will examine the interior angles of regular polygons. Work in groups then fill Reflect on this activity sheet

11. Class activity: Open and fill Reflections activity sheet, work out the answers in pairs Discuss discussion of solutions

12. Discussion and review Discuss and evaluate the effectiveness of the lesson plan and assessment in order to review the interior, exterior and central angles in polygons