Midsegment

A midsegment is the segment that connects the midpoints of the legs of a trapezoid.

Trapazoid A B C D has midpoint F for leg B C and midpoint E for A D. Points E and F form a line parallel to both bases

Midsegment Theorem

Thoerem: The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of its bases.

midsegment length = half the sum of the base lengths. Effectively the average

You can use this theorem to:

  • Find the length of a base given the length of the midsegment and other base
  • Find the length of the midsegment given the lengths of the bases
  • Verify that a segment is the midsegment given the slopes of the bases and their lengths

Example #2

Find the length of the midsegment EF.

Trapazoid A B C D has base A B of length 7 and base C D of length 15

Since EF is a midsegment, we know its length is one half the sum of the length of the bases. So,

E F = (A B + D C) over 2 Set up the equation

E F = (7 + 15) over 2 Substitute the measures of the bases into the formula

E F = 22 over 2 Simplify the numerator

EF = 11 Divide to solve

Your Turn!

Find the missing base.

In this case, we know one base and the midsegment. However, we can still use the formula for finding the length of the midsegment to find the missing base length.

midsegment = base sub1 + base sub2 / 2

Using this formula. Blank = (blank + D C) over 2 Set up the equation

Answer: EF, AB

blank = (blank + D C) over 2 Substitute the measures of the bases into the formula

Answer: 12, 5

___ = 5 + DC Multiply both sides by 2 to eliminate the denominator.

Answer: 24

___ = 5 + DC

Answer: 19

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