**Bases** - The two parallel lines are called the bases

**The Legs** - The two non parallel lines are the legs.

### Adjacent Angles of Trapezoid

The angles on the same side of a leg are called adjacent angles such as $$\angle A $$ and $$ \angle D $$ are supplementary. For the same reason, $$ \angle B $$ and $$ \angle C $$ are supplementary.

**Practice** Problem

$$ \angle ZWX = 180 − 44 = 136° $$

$$ \angle MLO = 180-124 = 56° $$

If LMNO is a trapezoid and its bases LO and MN are parallel then, $$ \angle MNO $$ and $$ \angle NOL $$ which must be supplementary however, the sum of these angles is not 180 111 + 68 ≠ 180

### Area of Trapezoid

- Area = 7 × ½(4 +8)
- 7 × ½(12)
- 7 ×6
- 42 square feet

### Midsegment of Trapezoid

The midsegment of a trapezoid is:

- parallel to both bases
- has length equal to the average of the length of the bases

To calculate the length of the midsegment find the average of the bases length of midsegment = (6+4)/2 = 5

The midsegment of a trapezoid is the segment that joins the midpoints of the nonparallel sides of a trapezoid.

In the trapezoid below, the midpoints of the non-parallel sides are points S and V. The midsegment is the red line segment from S to V.

The midsegment below can be found by

- calculating the lengths of the bases
- calculating the sum of the bases
- 9+45 = 54

- Dividing the sum by 2
- ½(54) = 27

The length of the midsegment is 26.5

Length of top base = 17-8 = 9

Length of bottom base = 20-0 =20

Sum of bases = 9 + 20 = 29

Divide sum of bases by 2 = ½(29) = 14.5

Therefore, the midsegment SV is 14.5 in length.

It is not a true midsegment because its length does **not** equal half the sum of the lengths of the bases.