what's the name of the theorem:median of right-triangle hypotenuse is always half of it This question is related to one of my previous questions.
The answer to that question included a theorem: "The median on the hypotenuse of a right triangle equals one-half the hypotenuse".
When I wrote the answer out and showed it a friend of mine, he basically asked me how I knew that the theorem was true, and if the theorem had a name.
So, my question:
-Does this theorem have a name?
-If not, what would be the best way to describe it during a math test? Or is it better to write out the full prove every time?

Let us consider the right triangle ABC with the right angle  and let AD be the median drawn from the vertex A to the hypotenuse 
BC. We need to prove that the length of the median AD is half the 
length of the hypotenuse BC. 
Draw the straight line DE passing through the midpoint D parallel to the 
leg AC till the intersection with the other leg AB at the point E. The angle BAC is the right angle by the condition. The angles BED and BAC are congruent as they are corresponding angles at the parallel lines AC and ED and the transverse. AB Therefore, the angle BED is the right angle. 
Now, since the straight line DE passes through the midpoint D and is parallel to AC, it cuts the side AB in two congruent segments of equal length: AE = EB 
So, the triangles AED and BED are right triangles that have congruent  AE and EB and the common DE. Hence, these triangles are congruent in accordance to the postulate  (SAS)  It implies that the segments AD and DB are congruent as corresponding sides of these triangles.
Since DB has the length half the length of the hypotenuse BC, we have proved that the median AD has the length half the length of the hypotenuse. 
