What is the Midsegment theorem of a trapezoid?

The midsegment of a trapezoid calculator, allows you to obtain the length of the midsegment or median of a trapezoid. The median of a trapezoid is a line parallel to the bases placed in the midpoint between them. With this tool, you will learn the midsegment of a trapezoid formula and how to find the midsegment of any trapezoid.

The median or midsegment of a trapezoid is a line parallel to the trapezoid's bases, which crosses the midpoint between them. It extends from one non-parallel side to the other.

A trapezoid with abcd sides.

Given the length of one base, you can use the midsegment to find the length of the other. Let's take a look at the midsegment of a trapezoid formula to learn how.

The median or midsegment of an ABCD trapezoid formula is straightforward. We just need the length of each of the bases ($AB$ and $CD$), add them, and then divide the result by two:

Midsegment=AB+CD2\text{Midsegment} = \frac{AB+CD}{2}Midsegment=2AB+CD​

This is the same as finding the median or average value between the bases, hence the name. If you find any two variables, you can obtain the other with ease by replacing the values in the equation above, or simply use the midsegment of a trapezoid calculator, and it will do the work for you 😉.

To find the midsegment of a trapezoid:

1. Measure and write down the length of the two parallel bases.
2. Add the two numbers.
3. Divide the result by two. This is the length of the midsegment.

You can verify the result with the midsegment of a trapezoid calculator or take a look at our trapezoid calculator to learn more.

A trapezoid has only one midsegment. The midsegment is a line that extends from one non-parallel side to the other, is parallel to the bases, and is placed at the midpoint between them.

The midsegment of a trapezoid with 2 cm bases is 2 cm. The formula for the midsegment is (AB + CD) / 2, and since AB and CD are identical, the result and the bases' lengths are equal in number.

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The midsegment of a trapezoid is parallel to each base, and its measure is half the sum of the lengths of the bases.

The following relation holds true for midsegment FE.

FE∥AB∥DC and FE=21​(AB+CD)

Let $ABCD$ be a trapezoid and FE be its midsegment. By definition, the midsegment of a trapezoid connects the midpoints of the nonparallel sides.

Next, draw the line connecting the points $C$ and $F,$ then extend the base AB such that it intersects with CF. Let $G$ be the point of intersection between these two lines.

By the Vertical Angles Theorem, it is given that $\angle AFG$ and $\angle CFD$ are congruent angles. Also, since GB and CD are parallel, then $\angle GAF$ and $\angle D$ are congruent angles by the Alternate Interior Angles Theorem.

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