Altitude

An altitude is the shortest distance from a vertex of a geometric figure to a line containing the opposite side (2-D) or the base (3-D).^[2] The altitude is always perpendicular to the opposite side. The foot of an altitude is the point where the altitude intersects the line containing the opposite side.

Manipulative 1 shows the altitudes of a triangle. Click on the blue points and drag them to change the figure. The red lines are the altitudes. The dotted lines are the lines which contain the opposite side. The feet of the altitude are the purple dots. Click on the reset button to return the manipulative to its original configuration.

Discovery

• For what type of triangle is the foot of an altitude not on the leg of the triangle?
• For what type of triangle does an altitude coincide with a leg of the triangle?
• For what type of triangle does an altitude intersect the opposite side?