document.write( "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
\n" ); document.write( "to prove the theorem . \n" ); document.write( "

Algebra.Com's Answer #628090 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "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:\r
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\n" ); document.write( "\n" ); document.write( "Figure 1
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\n" ); document.write( "\n" ); document.write( "Using the Midpoint formulae, the coordinates of the endpoints of the median are established as shown in figure 2:\r
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\n" ); document.write( "\n" ); document.write( "Figure 2:
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\n" ); document.write( "\n" ); document.write( "Since the line segments forming the bases and the median are horizontal lines, the measures can be determined by simple differences of the

-coordinates.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it\r
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