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Trapezoid

A trapezoid is a quadrilateral with one pair of parallel lines

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. .
Trapezoid Picture

 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.
Angles of a Trapezoid


Use the adjacent angles theorem to ddetermine m ZWX
Measure of angle
Adjacent angles of trapezoid
Use adjacent angles theorem to calculate mMLO.
Answer
Base angles of trapezoid
Find the value of x in the trapezoid below, then determine the measure of angles angle symbolWXY and XYZ
Answer
Same Side interior angles of trapezoid
What is wrong with trapezoid LMNO pictured below? (Explain why LMNO cannot be a trapezoid based on the information provided)Base angles of trapezoid

Answer
Area of Trapezoid
Trapezoid Area formulla

 Answer 
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


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  


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 (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

Trapezoid picture
Practice Problems

What is the length of midsegment SV in the trapezoid below?
Midsegment of trapezoid diagram and problem  answer 
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.