How To Find The Midsegment Of A Trapezoid

Midsegments of trapezoids

A trapezoid's midsegment connects its non-parallel sides

The midsegment of a trapezoid is a segment that connects the midpoints of the two non-parallel sides of a trapezoid.

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If ???\overline{AB}\parallel\overline{DC}???, if ???F??? is the midpoint of ???\overline{Advertizement}???, and if ???Eastward??? is the midpoint of ???\overline{BC}???, then ???\overline{Atomic number 26}??? is the midsegment of the trapezoid.

The human relationship between the length of the midsegment and the lengths of the parallel sides is

???Iron=\frac{ane}{ii}(AB+DC)???

The length of the midsegment of a trapezoid is always equal to one-half of the sum of the lengths of the parallel sides.

How to utilize the midsegment of a trapezoid to solve issues

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Finding the length of the side of the trapezoid, given the length of its midsegment

Example

In the trapezoid pictured, ???\overline{TU}\parallel\overline{WV}???, ???X??? is the midpoint of ???\overline{TW}???, and ???Y??? is the midpoint of ???\overline{UV}???. What is the length of ???\overline{WV}????

finding a side length using the length of the midsegment

By definition, ???\overline{XY}??? is the midsegment of the trapezoid. Therefore, nosotros know that

???XY=\frac{1}{2}(TU+WV)???

Let'due south plug in what we know and then solve for ???x???.

???29=\frac{1}{2}(23+2x+17)???

???29=\frac{1}{ii}(40+2x)???

???29=20+10???

???nine=x???

So the length of ???\overline{WV}??? is

???WV=2x+17???

???WV=two(9)+17???

???WV=35???

Midsegments of trapezoids for Geometry.jpg — The midsegment of a trapezoid is a segment that connects the midpoints of the 2 non-parallel sides of a trapezoid.

Instance

In the coordinate aeroplane, a trapezoid ???XYWZ??? has vertices at ???X=(-ii,2)???, ???Y=(3,2)???, ???Z=(-iii,-ii)???, and ???W=(4,-two)???. What is the length of the midsegment along the ???x???-centrality?

You tin plot the trapezoid and discover the lengths of the parallel sides.