Midsegment (Median) of a Trapezoid

The mid-segment of a trapezoid is the line segment mid-way between its two bases.  It is also called the median or the midline.

How many mid-segments does a trapezoid have?

A trapezoid has only one mid-segment since it has only 2 parallel sides and 2 non parallel sides.

The mid-segment bisects the non parallel sides. In other words, a mid-segment is the mid-way between the two bases.

The next segment will help you find the mid-segment of a trapezoid.

Formula

The basic formula to find the mid-segment of a trapezoid is given below:

Find the length of the mid-segment of the trapezoid given.

Solution:

As we know,
Mid-segment (M) = ½(a + b), here a = 23 cm, b = 14 cm
∴ M = ½(23 + 14)
= 18.5 cm

In trapezoid PQRS, what is the length of mid-segment XY.

Solution:

As we know,
Mid-segment (M) = ½(27 + 12), here a = 27 cm, b = 12 cm
∴ M = ½(27 + 12)
= 19.5 cm

Trapezoid Midsegment Theorem

The trapezoid mid-segment theorem states that a line connecting the midpoints of the non-parallel sides (legs) is parallel to the bases. It measures half the sum of lengths of the bases.

Trapezoid Midsegment Theorem Proof

Prove that the line connecting the midpoints of the legs of a trapezoid ABCD is parallel to the bases and half the sum of lengths of the bases.

To prove:

EF ∥AD, EF ∥BC

Proof:

AB ∥ CD, AE  ≅ EB, DF ≅ FC
AF and BC produced to point P