How to construct the orthocenter of a triangle.
How to construct the circumcenter using a compass and straightedge.
How to construct a perpendicular line at a point on a line.
How to define a midsegment in a triangle.
How to define and construct an angle bisector.
How to construct a midpoint and how to define a perpendicular bisector.
How to derive the area of a triangle formula using the rectangle area formula.
How to define an altitude and draw them on acute, right, and obtuse triangles.
How to construct the incenter using a compass and straightedge.
How to classify a triangle based on its side lengths and angle measures.
How to define a median in a triangle.
How to apply the triangle angle sum theorem.
How to determine if two triangles in a circle are similar and how to prove that three similar triangles exist in a right triangle with an altitude.
How to identify the centroid and the way it divides each of the medians.
How to use Pascal's triangle.
How to calculate the area of any triangle using two sides and an included angle.