How to define a midsegment in a triangle.
How to calculate the hypotenuse in a right triangle given the lengths of the legs using the Pythagorean Theorem.
How to define isosceles triangles, their components and how to determine their properties.
How to determine the triangle side inequalities.
How to determine the relationship between the side inequalities and angle inequalities in a triangle.
Understanding why the area of a triangle is 1/2 base times height
How to use a counterexample to prove a definition or conjecture incorrect.
How to use the fundamental theorem of calculus to compute the net change of a quantity.
Overview of similarity: congruent angles, proportional corresponding sides
How to understand the idea of slope.
Understanding the science of physics.
How to define an inverse.
How to define an antiderivative.
How to define the derivative of a function at a point x=a.
How to derive the distance formula for polar coordinates.
How can we balance individual rights with the public good?
How to prove two triangles are similar using a line parallel to a base.
How to solve a simple sine equation: sin (theta) = 1/2.