An altitude of a triangle is a line segment from one of its vertices which meets the opposite side at a right angle.

The altitudes of a triangle are the Cevians A_i H_i that are perpendicular to the legs A_j A_k opposite A_i. The three altitudes of any triangle are concurrent at the orthocenter H. This fundamental fact did not appear anywhere in Euclid's Elements. The triangle Δ H_1 H_2 H_3 connecting the feet of the altitudes is known as the orthic triangle.

Cevian | maltitude | orthic triangle | orthocenter | perpendicular | perpendicular foot | Taylor circle

middle school level (California grade 7 standard)