Middle segment of a trapezoid - Examples, Exercises and Solutions

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
ABEFDCAB∥EF∥DC
EF=AB+DC2EF=\frac{AB+DC}{2}


Suggested Topics to Practice in Advance

  1. Midsegment of a triangle

Practice Middle segment of a trapezoid

Exercise #1

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

Video Solution

Answer

Exercise #2

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

Video Solution

Answer

Not true

Exercise #3

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

Video Solution

Answer

No

Exercise #4

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

Video Solution

Answer

Exercise #5

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

Video Solution

Answer

True

Exercise #1

The quadrilateral ABCD is a trapezoid.

EF is the midsegment.

Calculate EF.

333999AAABBBDDDCCCFFFEEE

Video Solution

Answer

6

Exercise #2

The quadrilateral ABCD is a trapezoid.

EF is the midsection.

Calculate CD.

888121212AAABBBDDDCCCFFFEEE

Video Solution

Answer

16

Exercise #3

EF is the midsegment of the trapezoid ABCD.

Calculate the length of EF.

999151515AAABBBDDDCCCFFFEEE

Video Solution

Answer

12

Exercise #4

EF is the midsegment of the trapezoid ABCD.

Calculate the length of EF.

888141414AAABBBDDDCCCFFFEEE

Video Solution

Answer

11

Exercise #5

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

Find X

XXX666444AAABBBDDDCCCFFFEEE

Video Solution

Answer

2

Exercise #1

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

Find X

XXX151515121212AAABBBDDDCCCFFFEEE

Video Solution

Answer

9

Exercise #2

The quadrilateral ABCD is an isosceles trapezoid.

EF the midsegment.

Calculate the length of X.

222222XXXAAABBBDDDCCCFFFEEE

Video Solution

Answer

11

Exercise #3

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

Find X

XXX777AAABBBDDDCCCFFFEEE

Video Solution

Answer

7

Exercise #4

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

Find X

XXX777555AAABBBDDDCCCFFFEEE

Video Solution

Answer

3

Topics learned in later sections

  1. Midsegment