The three altitudes of a triangle meet at one point (orthocenter)

Dependencies: Through a point off a line, exactly one parallel exists (Playfair) (Through a point off a line, exactly one parallel exists (Playfair)), opposite sides of a parallelogram are equal (Parallelogram properties (opposite sides equal, diagonals bisect each other)), Three perpendicular bisectors meet (circumcenter) (Three perpendicular bisectors meet (circumcenter)).

Statement

Let $\triangle ABC$. Drop a perpendicular from each of $A$, $B$, $C$ to the line containing the opposite side; the three perpendiculars (i.e. the three altitudes) meet at a single point. This point is called the orthocenter of $\triangle ABC$, denoted $H$.