How to define point of concurrency; how to identify the four main points of concurrency in triangles.
How to construct a perpendicular line at a point on a line.
How to describe and label point, line, and plane. How to define coplanar and collinear.
How to construct the incenter using a compass and straightedge.
How to construct the orthocenter of a triangle.
How to construct the circumcenter using a compass and straightedge.
How to identify the centroid and the way it divides each of the medians.
How to define and label a line segment.
How to find the shortest distance between a point and a line.
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 define a circle and a sphere using the word locus.
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 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.