SOLUTION: theorem 6. the median of a trapezoid to each base and its lenght is one half the sum of the lenghts of the bases to prove the theorem .

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Question 1012206: theorem 6. the median of a trapezoid to each base and its lenght is one half the sum of the lenghts of the bases
to prove the theorem .
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(53862) About Me  (Show Source):
You can put this solution on YOUR website!
.
the median of a trapezoid to each base and its lenght is one half the sum of the lenghts of the bases
to prove the theorem
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See the lesson Trapezoids and their mid-lines in this site.
The Theorem and the proof are there.

One note: this line is called the mid-line of a trapezoid, not the median.


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Since the shape and size of a plane figure is invariate under coordinate translations and rotations, a general trapezoid can be placed with one vertex at the origin and one base coincident with the -axis without loss of generality. See figure 1:

Figure 1


Using the Midpoint formulae, the coordinates of the endpoints of the median are established as shown in figure 2:

Figure 2:


Since the line segments forming the bases and the median are horizontal lines, the measures can be determined by simple differences of the -coordinates.

The measure of the lower base is simply , the measure of the upper base is . Half of the sum of the bases is then . Compare with the measure of the median: Q.E.D.

John

My calculator said it, I believe it, that settles it