How to apply the triangle angle sum theorem.
How to label an angle and how to differentiate between acute, right, obtuse, and straight angles.
How to derive the formula to find the sum of angles in any polygon.
How to define adjacent angles.
How to use the power reduction formulas to derive the half-angle formulas.
How to determine the relationship between the side inequalities and angle inequalities in a triangle.
How to identify, define, and label rays and opposite rays.
How to use the sine and cosine addition formulas to prove the double-angle formulas.
How to define and identify vertical angles.
How to identify a segment from the vertex angle in an isosceles triangle to the opposite side.
How to derive two more cosine double-angle formulas.
How to define and construct an angle bisector.
How to find the angle between planes, and how to determine if two planes are parallel or perpendicular.
How to define a central angle and find the measure of its intercepted arc; how to describe the intercepted arcs of congruent chords.
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 describe same side interior and same side exterior angles and their special properties.
How to identify all of the special properties of parallelograms and use them to solve problems.