How to derive the formula for the midpoint of a segment in three dimensions.
How to derive the equation for the distance between two points using the Pythagorean Theorem.
How to define and construct an angle bisector.
How to construct the circumcenter using a compass and straightedge.
How to define the components of a vector.
How to identify a segment from the vertex angle in an isosceles triangle to the opposite side.
How to find the resultant of two forces when they are parallel, opposite, or perpendicular in direction.
How to define a polygon, how to distinguish between concave and convex polygons, how to name polygons.
How to identify the centroid and the way it divides each of the medians.
How to define a rhombus and compare it to a square and rectangle.
How to define a tangent line; how to determine the angle a radius to a tangent forms.
How to find the midpoint of a segment with endpoints in rectangular coordinates, How to write the midpoint formula.
How to understand what vectors are, and how they can be represented geometrically.
How to define point of concurrency; how to identify the four main points of concurrency in triangles.
How to identify a kite and its special properties.
How to derive the area formula of a kite based on the rectangle formula; how to calculate the area of a rectangle using diagonal lengths.