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 Trapezoid Picture Example 2 of legs and the Bases base and legs of trapezoid

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.

Adjacent Angles of a Trapezoid are supplementary

Practice Problem

Problem 1

Use the adjacent angles theorem to determine m $$ \angle ZWX $$

Adjacent angles of trapezoid

$$ \angle ZWX = 180 − 44 = 136° $$

Problem 2

Use adjacent angles theorem to calculate m $$ \angle MLO $$

Base angles of trapezoid

$$ \angle MLO = 180-124 = 56° $$

Problem 3

Find the value of x in the trapezoid below, then determine the measure of angles $$ \angle WXY $$ and $$ \angle XYZ $$

Same Side interior angles of trapezoid
Problem 4

What is wrong with trapezoid LMNO pictured below? (Explain why LMNO cannot be a trapezoid based on the information provided)

Base angles of trapezoid

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

Trapezoid Area formulla
Problem 5
  • 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

Problem 6

Use the midsegment theorem to determine the length of midsegment ON

Parallelogram Sides Picture

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

Problem 7
Quick REVIEW of Midpoint

The midpoint of the red segment pictured on the left is the point (A, 2b). The most important thing to remember is that a midpoint bisects a line (cuts a line into two equal halves).

Parallelogram Sides Picture

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.

Midsegment of Trapezoid, Picture

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

Trapezoid picture
Problem 8

What is the length of midsegment SV in the trapezoid below?

Midsegment of trapezoid diagram and problem

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.

Problem 9

Is the reg segment below a midsegment?

Trapezoid Brain Teaser

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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