Trapezoid

A trapezoid is a quadrilateral with one pair of parallel lines.

Bases

The two parallel lines are called the bases. In the picture below, BC and AD are the bases.

The Legs

The two non parallel lines are the legs. In this picture, the legs are AB and CD.

 Adjacent Angles of Trapezoid  

The angles on the same side of a leg are called adjacent angles such as NML and MLO are supplementary. For the same reason, MNO and NOL are supplementary.

Use the adjacent angles theorem to ddetermine m ZWX

ZWX = 180 − 44 = 136°

Measure of angle

Use adjacent angles theorem to calculate mMLO.

Answer

MLO = 180-124 = 56°

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

Answer

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

Answer

If LMNO is a trapezoid and its bases LO and MN are parallel then, MNO and NOL which must be supplementary

however, the sum of these angles is not 180
111 + 68 ≠ 180

Area of Trapezoid

 Answer 

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

Midsegment of Trapezoid

The midsegment of a trepzoid is

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

Use the midsegment theorem to determine the length of midsegment ON.

Midsegment's Length

To calculate the length of the midsgement find the average of the bases

length of midsegment= (6+4)/2 = 5

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).  Show Midpoint  

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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 (lenght 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

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

Is the reg segment below a midsegment?

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