The altitudes of a triangle meet

An altitude of a triangle is a line from one vertex to the other side which is at right angles (perpendicular) to the side.

The altitudes of a triangle always meet at a point called the orthocentre.

Proof

For each vertex of the triangle, draw a line through it parallel to the opposite side of the triangle.

These lines form a larger triangle. The altitudes of the original triangle are coincident with the perpendicular bisectors of the larger triangle, and thus, by Proof that the bisectors of the sides of a triangle meet they meet at the circumcentre of the larger triangle.