Midsegment of a Trapezoid Practice Problems & Solutions

Master trapezoid midsegment properties with step-by-step practice problems. Learn parallel lines, midpoint calculations, and length formulas through guided exercises.

📚What You'll Master with These Trapezoid Midsegment Problems
  • Apply the midsegment formula EF = (AB + DC)/2 to find missing lengths
  • Identify and prove midsegment properties using parallel line theorems
  • Calculate midpoint coordinates when trapezoid vertices are given
  • Solve for unknown side lengths using midsegment relationships
  • Prove that midsegments divide non-parallel sides into equal parts
  • Apply midsegment properties to solve real-world trapezoid problems

Understanding Midsegment of a Trapezoid

Complete explanation with examples

The midsegment of a trapezoid divides into two equal parts the two sides from which it extends and, in addition, is parallel to both bases of the trapezoid and measures half the length of these.
Let's see the properties of the midsegment of a trapezoid in the following illustration:

1- Let's see the properties of the midsegment in an illustration

If EFEF Midsegment
then:
AE=DEAE=DE
BF=CFBF=CF
AB∥EF∥DCAB∥EF∥DC
EF=AB+DC2EF=\frac{AB+DC}{2}

Detailed explanation

Practice Midsegment of a Trapezoid

Test your knowledge with 3 quizzes

The quadrilateral ABCD is a trapezoid, EF is the middle section.

Find X

XXX777555AAABBBDDDCCCFFFEEE

Examples with solutions for Midsegment of a Trapezoid

Step-by-step solutions included
Exercise #1

Below is an isosceles trapezium.

EF is parallel to the base of the trapezium.

True or false: EF is the midsection of the trapezoid.

AAABBBDDDCCCEEEFFF

Step-by-Step Solution

Answer:

True

Video Solution
Exercise #2

Given an isosceles trapezoid, is the dashed segment a middle segment of the trapezoid?

Step-by-Step Solution

Answer:

Not true

Video Solution
Exercise #3

In which figure is the dashed line the midsection of the trapezoid?

Step-by-Step Solution

Answer:

Video Solution
Exercise #4

In which figure is the dotted line the midsegment in the trapezoid?

Step-by-Step Solution

Answer:

Video Solution
Exercise #5

Is the dashed segment the midsegment of the isosceles trapezoid below?

Step-by-Step Solution

Answer:

No

Video Solution

Frequently Asked Questions

Everything you need to know about Midsegment of a Trapezoid

What is the midsegment of a trapezoid formula?

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The midsegment formula is EF = (AB + DC)/2, where EF is the midsegment length and AB, DC are the parallel bases. The midsegment is always parallel to both bases and equals half their sum.

How do you prove a line is the midsegment of a trapezoid?

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You can prove a line is a midsegment by showing: 1) It connects midpoints of non-parallel sides, OR 2) It passes through one midpoint and is parallel to a base. Either condition proves it's the midsegment.

What are the three main properties of trapezoid midsegments?

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The three key properties are: 1) Parallel to both bases (AB∥EF∥DC), 2) Divides non-parallel sides equally (AE=DE, BF=CF), 3) Length equals average of bases (EF = (AB+DC)/2).

How do you find the length of a trapezoid base using the midsegment?

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Use the formula EF = (AB + DC)/2 and solve for the unknown base. If you know the midsegment length and one base, multiply the midsegment by 2, then subtract the known base to find the unknown base.

Can a trapezoid have more than one midsegment?

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No, a trapezoid has exactly one midsegment. It's the unique line segment connecting the midpoints of the two non-parallel sides (legs) of the trapezoid.

What's the difference between triangle and trapezoid midsegments?

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Triangle midsegments connect midpoints of two sides and equal half the third side. Trapezoid midsegments connect midpoints of non-parallel sides and equal half the sum of both parallel bases.

How do you solve trapezoid midsegment word problems step by step?

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Follow these steps: 1) Identify given information and what to find, 2) Draw and label the trapezoid, 3) Apply the midsegment formula EF = (AB+DC)/2, 4) Substitute known values and solve algebraically, 5) Check your answer makes geometric sense.

Why is the trapezoid midsegment parallel to both bases?

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The midsegment is parallel to both bases due to the midpoint theorem. Since it connects midpoints of the legs and the bases are already parallel, the midsegment must be parallel to both bases by the properties of similar triangles formed.

Continue Your Math Journey

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