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Midsegments of Triangles
Skill 25
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Objective HSG-SRT.5: Students are responsible for using properties of Midsegments to solve problems.
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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 πͺπ¨ , and E is the midpoint of πͺπ© Then π«π¬ β₯ π¨π© and ππ= π π π¨π©
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Example 1; Identifying Parallel Segments
What are three pairs of parallel segments in βπ·πΈπΉ? Since R is the midpoint of π«π¬ and S is the midpoint of π¬π D E F T S R πΉπΊ β₯ π«π Since R is the midpoint of π«π¬ and T is the midpoint of π«π πΉπ» β₯ π¬π Since S is the midpoint of π¬π and T is the midpoint of π«π πΊπ» β₯ π¬π«
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Example 2; Finding Lengths
In βπππ T, U, and B are midpoints. What are the lengths of ππ , ππ΅ , and ππ
? U B T S R Q 40 30 50 π»πΌ= π π πΊπΉ π»πΌ= π π ππ π»πΌ=ππ πΌπ©= π π πΈπΊ πΌπ©= π π ππ πΌπ©=ππ π»π©= π π πΈπΉ ππ = π π πΈπΉ π ππ = πΈπΉ πΌπ©=ππ
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Example 3; Using the Midsegment of a Triangle
A geologist wants to determine the distance, π΄π΅, across a sinkhole. Choosing a point E outside the sinkhole, she finds the distance π΄πΈ and π΅πΈ. She locates the midpoints C and D of π΄πΈ and π΅πΈ and then measures πΆπ· . What is the distance across the sinkhole? A B C D E She measures πͺπ«=ππ ππ. πͺπ«= π π π¨π© π¨π©=π πͺπ« π¨π©=π ππ π¨π©=ππ ππππ 46β
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Example 4; Using the Midsegment of a Triangle
πΆπ· is a bridge being built over a lake as shown in the figure at the left. What is the length of the bridge? Notice: πͺ is a midpoint Notice: π« is a midpoint πͺπ«= π π ππππ πͺπ«=ππππ ππππ 963 ft. 2640 ft. C D
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#25: Midsegments in Triangles
Questions? Summarize Notes Homework Video Quiz
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