Middle segment of a triangle - Examples, Exercises and Solutions

The midsegment of a triangle has three main properties:

  • The midsegment crosses exactly through the middle of the two sides that determine it.
  • The midsegment is parallel to the third side of the triangle.
  • The midsegment measures half the length of the side arranged parallel to it.

Let's look at the properties of the midsegment of a triangle in the following illustration:

Midsegment of a triangle

If AD=CD AD=CD
AE=BEAE=BE

then 2DE=CB2DE=CB
DE∥CBDE∥CB

Detailed explanation

Practice Middle segment of a triangle

Question 1

Given that DE is a middle section in triangle ABC, what is the length of side DE?

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Question 2

Given that DE is a middle section in triangle ABC, what is the length of side DE?

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Question 3

Given that DE is a middle section in triangle ABC, what is the length of side DE?

121212999121212AAABBBCCCDDDEEE

Question 4

Given that DE is a middle section in triangle ABC, what is the length of side DE?

181818121212181818AAABBBCCCDDDEEE

Question 5

Given that DE is a middle section in triangle ABC, what is the length of side DE?

222222666222222AAABBBCCCEEEDDD

examples with solutions for middle segment of a triangle

Exercise #1

Given that DE is a middle section in triangle ABC, what is the length of side DE?

666888101010AAABBBCCCEEEDDD

Video Solution

Answer

4

Exercise #2

Given that DE is a middle section in triangle ABC, what is the length of side DE?

444666101010AAABBBCCCDDDEEE

Video Solution

Answer

5

Exercise #3

Given that DE is a middle section in triangle ABC, what is the length of side DE?

121212999121212AAABBBCCCDDDEEE

Video Solution

Answer

4.5

Exercise #4

Given that DE is a middle section in triangle ABC, what is the length of side DE?

181818121212181818AAABBBCCCDDDEEE

Video Solution

Answer

9

Exercise #5

Given that DE is a middle section in triangle ABC, what is the length of side DE?

222222666222222AAABBBCCCEEEDDD

Video Solution

Answer

11

Question 1

Given that DE is the middle section in triangle ABC, what is the length of side DE?

141414111111181818AAABBBCCCDDDEEE

Question 2

Given that DE is the middle section in triangle ABC, what is the length of side DE?

121212242424242424AAABBBCCCDDDEEE

Question 3

Given that DE is the middle section in triangle ABC, what is the length of side DE?

171717303030303030AAABBBCCCDDDEEE

Question 4

Given that DE is the middle section in triangle ABC, what is the length of side DE?

151515212121212121AAABBBCCCDDDEEE

Question 5

Given that DE is the middle section in triangle ABC, what is the length of side DE?

121212141414111111AAABBBCCCDDDEEE

examples with solutions for middle segment of a triangle

Exercise #1

Given that DE is the middle section in triangle ABC, what is the length of side DE?

141414111111181818AAABBBCCCDDDEEE

Video Solution

Answer

7

Exercise #2

Given that DE is the middle section in triangle ABC, what is the length of side DE?

121212242424242424AAABBBCCCDDDEEE

Video Solution

Answer

6

Exercise #3

Given that DE is the middle section in triangle ABC, what is the length of side DE?

171717303030303030AAABBBCCCDDDEEE

Video Solution

Answer

15

Exercise #4

Given that DE is the middle section in triangle ABC, what is the length of side DE?

151515212121212121AAABBBCCCDDDEEE

Video Solution

Answer

7.5

Exercise #5

Given that DE is the middle section in triangle ABC, what is the length of side DE?

121212141414111111AAABBBCCCDDDEEE

Video Solution

Answer

7

Question 1

Given that DE is the middle section in triangle ABC, what is the length of side DE?

262626303030242424AAABBBCCCDDDEEE

Question 2

Given that DE is the middle section in triangle ABC, what is the length of side DE?

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Question 3

In which figure is the dashed segment the median?

Question 4

In which figure is the dashed segment the median?

Question 5

The quadrilateral ABCD is a trapezoid.

EF is the midsegment.

Calculate the length of side CD.

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examples with solutions for middle segment of a triangle

Exercise #1

Given that DE is the middle section in triangle ABC, what is the length of side DE?

262626303030242424AAABBBCCCDDDEEE

Video Solution

Answer

12

Exercise #2

Given that DE is the middle section in triangle ABC, what is the length of side DE?

888121212111111AAABBBCCCDDDEEE

Video Solution

Answer

4

Exercise #3

In which figure is the dashed segment the median?

Video Solution

Answer

Exercise #4

In which figure is the dashed segment the median?

Video Solution

Answer

Exercise #5

The quadrilateral ABCD is a trapezoid.

EF is the midsegment.

Calculate the length of side CD.

888121212AAABBBDDDCCCFFFEEE

Video Solution

Answer

16

Topics learned in later sections

  1. Midsegment
  2. Midsegment of a trapezoid