How to define circumscribed and inscribed circles and polygons relative to each other.
How to calculate the measure of an inscribed angle.
How to define a polygon, how to distinguish between concave and convex polygons, how to name polygons.
How to define the apothem and center of a polygon; how to divide a regular polygon into congruent triangles.
Naming polygons, classifying triangles, and classifying quadrilaterals
How to determine the number of diagonals in a polygon.
How to find the sum of the exterior angles in a polygon and find the measure of one exterior angle in an equiangular polygon.
How to derive the formula to find the sum of angles in any polygon.
How to derive the formula to calculate the area of a regular polygon.
How to find the measure of one angle in any equiangular or regular polygon.
How to convert between length and area ratios of similar polygons
How to calculate the surface area of any pyramid, emphasizing regular polygons as bases.
How to prove that an angle inscribed in a semicircle is a right angle; how to solve for arcs and angles formed by a chord drawn to a point of tangency.
How to identify if two figures are similar.
How to find the length of tangent segments drawn to a circle from the same point.
How to calculate the area between a square and an inscribed circle.
How to find the volume of any pyramid.
How to prove that opposite angles in a cyclic quadrilateral are congruent; how to prove that parallel lines create congruent arcs in a circle.
How to determine if two triangles in a circle are similar and how to prove that three similar triangles exist in a right triangle with an altitude.
How to strategize about solving a problem with trapezoidal arches.