1. Midsegments of Triangles
Skill 26

2. Objective
HSG-SRT.5: Students are responsible for using properties of Midsegments to solve problems.

3. Theorem 23: Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half as long. C E D A B
If D is the midpoint of 𝑪𝑨 ,
and E is the midpoint of 𝑪𝑩
Then 𝑫𝑬 ∥ 𝑨𝑩 and 𝐃𝐄= 𝟏 𝟐 𝑨𝑩

4. Example 1; Identifying Parallel Segments
What are three pairs of parallel segments in ∆𝐷𝐸𝐹?
Since R is the midpoint of 𝑫𝑬 and S is the midpoint of 𝑬𝑭 D E F T S R
𝑹𝑺 ∥ 𝑫𝑭
Since R is the midpoint of 𝑫𝑬 and T is the midpoint of 𝑫𝑭
𝑹𝑻 ∥ 𝑬𝑭
Since S is the midpoint of 𝑬𝑭 and T is the midpoint of 𝑫𝑭
𝑺𝑻 ∥ 𝑬𝑫

5. Example 2; Finding Lengths
In ∆𝑄𝑆𝑇 T, U, and B are midpoints. What are the lengths of 𝑇𝑈 , 𝑈𝐵 , and 𝑄𝑅 ? U B T S R Q 40 30 50
𝑻𝑼= 𝟏 𝟐 𝑺𝑹
𝑻𝑼= 𝟏 𝟐 𝟒𝟎
𝑻𝑼=𝟐𝟎
𝑼𝑩= 𝟏 𝟐 𝑸𝑺
𝑼𝑩= 𝟏 𝟐 𝟓𝟎
𝑼𝑩=𝟐𝟓
𝑻𝑩= 𝟏 𝟐 𝑸𝑹
𝟑𝟎 = 𝟏 𝟐 𝑸𝑹
𝟐 𝟑𝟎 = 𝑸𝑹
𝑼𝑩=𝟔𝟎

6. Example 3; Using the Midsegment of a Triangle
A geologist wants to determine the distance, 𝐴𝐵, across a sinkhole. Choosing a point E outside the sinkhole, she finds the distance 𝐴𝐸 and 𝐵𝐸. She locates the midpoints C and D of 𝐴𝐸 and 𝐵𝐸 and then measures 𝐶𝐷 . What is the distance across the sinkhole? A B C D E
She measures 𝑪𝑫=𝟒𝟔 𝒇𝒕.
𝑪𝑫= 𝟏 𝟐 𝑨𝑩
𝑨𝑩=𝟐 𝑪𝑫
𝑨𝑩=𝟐 𝟒𝟔
𝑨𝑩=𝟗𝟐 𝒇𝒆𝒆𝒕
46’

7. Example 4; Using the Midsegment of a Triangle
𝐶𝐷 is a bridge being built over a lake as shown in the figure at the left. What is the length of the bridge?
Notice: 𝑪 is a midpoint
Notice: 𝑫 is a midpoint
𝑪𝑫= 𝟏 𝟐 𝟐𝟔𝟒𝟎
𝑪𝑫=𝟏𝟑𝟐𝟎 𝒇𝒆𝒆𝒕
963 ft.
2640 ft. C D

8. #26: Midsegments in Triangles
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