How to construct a perpendicular line at a point on a line.
How to write a good definition that does not have a counterexample.
How to define point of concurrency; how to identify the four main points of concurrency in triangles.
How to describe and label point, line, and plane. How to define coplanar and collinear.
How to define a circle and a sphere using the word locus.
How to use a counterexample to prove a definition or conjecture incorrect.
How to use inverse trig functions to find angles in right triangles.
How to define and label a line segment.
How to construct the incenter using a compass and straightedge.
How to construct the orthocenter of a triangle.
How to find the shortest distance between a point and a line.
How to construct the circumcenter using a compass and straightedge.
How to define rotational symmetry and identify the degree of rotational symmetry of common regular polygons.
How to find the length of tangent segments drawn to a circle from the same point.
How to derive the equation for the distance between two points using the Pythagorean Theorem.
How to identify the centroid and the way it divides each of the medians.
How to define a tangent line; how to determine the angle a radius to a tangent forms.
How to define a rotation and what information is necessary to perform a rotation.
How to determine the number of handshakes possible in a group of a certain number of people.
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.