Trapezoid

A trapezoid is a quadrilateral with one pair of parallel lines

Bases - The two parallel lines are called the bases

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

Example 1 of legs and the Bases Example 2 of legs and the Bases

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
• 35-16 = 9 (length of upper base)
• 45-0 =45 (length of lower base)
• 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.

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