91Ó°ÊÓ

Prove that the diagonals of a parallelogram bisect each other.

Prove that the altitudes of a triangle are concurrent. (An altitude is a perpendicular from a vertex to the opposite side, possibly extended. The point of intersection is called the orthocentre of the triangle.)

Prove that the centroid, the circumcentre and the orthocentre of a triangle are collinear. (The line on which they all lie is called the Euler line.)