How to solve a simple proportion.
How to define the law of sines.
How to define and use the law of cosines.
How to write a good definition that does not have a counterexample.
How to prove two triangles are similar using a line parallel to a base.
How to use a counterexample to prove a definition or conjecture incorrect.
How to define a circle and a sphere using the word locus.
How to determine if two triangles are similar using a shortcut.
How to relate corresponding altitudes, medians and angle bisectors in similar triangles.
How to relate the sides of an angle bisected and the lengths of the opposite side.
How to identify the centroid and the way it divides each of the medians.
How to define a secant; how to find the length of various secants in circles.
How to identify if two figures are similar.
How to determine the types of transformations, the definition of isometry, and how to say and write a transformation's new image.