Before we talk on how a triangle's midsegment is important, we have to talk on how it's found. Well, to find the midsegment of a triangle, you have to find the midpoints of two of the triangle's side. Once you have found the two midpoints, you will connect them both with a line. That's it! You've just found the triangle's midsegment! One important thing to note is that the midsegment will always be parallel to the third side (the one you didn't connect midpoints with). So in total you can find three midsegments. What's very important about the midsegments, is that they will always be half the length of the third segment (the one you didn't connect midpoints with). To summarise, a triangle's midsegments are very useful to find the triangles side's length.
Note: on the triangle on top, the segment DE is half (length) of segment BC.
The midsegment on a trapezoid is found the same way as the triangle, but it will be parallel to the two remaining bases. Also it has the average length of both of the trapezoid's bases. The midsegment on a trapezoid divides it into two smaller trapezoids. This is important for each of the trapezoids will have half the altitude of the original one. With that in mind you will use the midsegment's length times the trapezoid's total altitude to find its area.
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