Midsegment of a Triangle - Examples, Exercises and Solutions

Question Types:
Midsegment of a Triangle: Calculating areaMidsegment of a Triangle: Calculating perimeterMidsegment of a Triangle: Identifying and defining elements

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 Midsegment of a Triangle

Question 1

Calculate the perimeter of triangle ADE given that DE is the midsegment of triangle ABC.

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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?

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Question 4

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

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Question 5

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

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Examples with solutions for Midsegment of a Triangle

Exercise #1

Calculate the perimeter of triangle ADE given that DE is the midsegment of triangle ABC.

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Video Solution

Step-by-Step Solution

In order to calculate the perimeter of triangle △ADE \triangle ADE we need to find the lengths of its sides,

Let's now refer to the given information that DE DE is a median in △ABC \triangle ABC and therefore a median in a triangle equals half the length of the side it does not intersect, additionally we'll remember the definition of a median in a triangle as a line segment that extends from the midpoint of one side to the midpoint of another side, we'll write the property mentioned (a) and the fact derived from the given definition (b+c):

a.

DE=12BC DE=\frac{1}{2}BC b.

AD=12AB AD=\frac{1}{2}AB c.

AE=12AC AE=\frac{1}{2}AC\\ Additionally, the given data in the drawing are:

d.

BC=8 BC=8 e.

AB=6 AB=6 f.

AC=10 AC=10 Therefore, we will substitute d', e', and f' respectively in a', b', and c', and we get:

g.

DE=12BC=12⋅8=4 DE=\frac{1}{2}BC=\frac{1}{2}\cdot8=4 h.

AD=12AB=12⋅6=3 AD=\frac{1}{2}AB=\frac{1}{2}\cdot6=3 i.

AE=12AC=12⋅10=5 AE=\frac{1}{2}AC=\frac{1}{2}\cdot10=5 888444333333555555AAABBBCCCDDDEEE

Therefore the perimeter of △ADE \triangle ADE is:

j.

PADE=DE+AD+AE=4+3+5=12 P_{ADE}=DE+AD+AE=4+3+5=12 Therefore the correct answer is answer d.

Answer

12

Exercise #2

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

181818121212181818AAABBBCCCDDDEEE

Video Solution

Answer

9

Exercise #3

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

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Video Solution

Answer

11

Exercise #4

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

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Video Solution

Answer

4.5

Exercise #5

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

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Video Solution

Answer

4

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 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?

151515212121212121AAABBBCCCDDDEEE

Question 4

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

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Question 5

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

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Exercise #6

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

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Video Solution

Answer

5

Exercise #7

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

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Video Solution

Answer

6

Exercise #8

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

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Video Solution

Answer

7.5

Exercise #9

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

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Video Solution

Answer

15

Exercise #10

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

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Video Solution

Answer

7

Question 1

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

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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

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

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Question 4

In which figure is the dashed segment the median?

Question 5

In which figure is the dashed segment the median?

Exercise #11

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

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Video Solution

Answer

12

Exercise #12

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

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Video Solution

Answer

4

Exercise #13

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

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Video Solution

Answer

7

Exercise #14

In which figure is the dashed segment the median?

Video Solution

Answer

Exercise #15

In which figure is the dashed segment the median?

Video Solution

Answer

Topics learned in later sections

  1. Midsegment
  2. Midsegment of a trapezoid