Midsegment Theorem.

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Presentation transcript:

Midsegment Theorem

Vocabulary The Midsegment of a Triangle is a segment that connects the midpoints of two sides of the triangle. D B C E A D and E are midpoints DE is the midsegment

Theorem 5.1 Midsegment Theorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. D B C E A

Example 1 In the diagram, ST and TU are midsegments of triangle PQR. Find PR and TU. 5 ft 16 ft TU = ________ PR = ________

Example 2 In the diagram, XZ and ZY are midsegments of triangle LMN. Find MN and ZY. 14 cm 53 cm ZY = ________ MN = ________

Example 3 In the diagram, ED and DF are midsegments of triangle ABC. Find DF and AB. 3X - 4 5X+2 x = ________ 10 DF = ________ 26 AB = ________ 52