Question 1012206
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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 *[tex \Large x]-axis without loss of generality.  See figure 1:


Figure 1
*[illustration fig1]


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


Figure 2:
*[illustration fig2]


Since the line segments forming the bases and the median are horizontal lines, the measures can be determined by simple differences of the *[tex \Large x]-coordinates.


The measure of the lower base is simply *[tex \Large a], the measure of the upper base is *[tex \Large c\ -\ b].  Half of the sum of the bases is then *[tex \Large \frac{a\ +\ c\ -\ b}{2}].  Compare with the measure of the median: *[tex \Large \frac{(a\ +\ c)}{2}\ -\ \frac{b}{2}\ =\ \frac{a\ +\ c\ -\ b}{2}]  Q.E.D.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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