The Midsegment of a Trapezoid

The midsegment of a trapezoid connects the midpoints of the non-parallel sides and is parallel to the bases (parallel sides).  Its length is the average of the base-lengths.

EXAMPLE 4:  Find the length of CD:

SOLUTION:  15 is the average of AB and CD, so

                                                                                   

We can multiply both sides of this equation by 2 and combine like terms on the left to get: 

So:

So x = –8 or x = 5

But x cannot be –8 since that would make 2x – 7 negative.

Therefore, CD = x2 + x – 3 = 25 + 5 – 3 = 27


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