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Definitions

Triangles come in two parts. The segments are called legs. The points where two segments meet is a vertex. This is similar to the vertex of an angle. In fact we customarily refer to the V-shaped parts of triangles as angles even though, technically, they aren't since our definition of an angle requires the sides to be rays, not segments.
In a right triangle the sides have special names. The side opposite the right angle is the hypotenuse. The other two sides are called the legs.
The altitude of a triangle is the segment connecting the vertex to the line through the opposite side that's also perpendicular to the line. Notice that in a right triangle both of the legs are altitudes. Notice in the figure to the right that the altitude doesn't have to be inside the triangle.

The median of a triangle is the segment connecting a vertex to the midpoint of the opposite side.