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The Midsegment Theorem

Learn the fundamentals and applications of the Triangle Midsegment Theorem with clear examples and exercises. Understand how midsegments work in triangles and their relationships with sides and lengths. Enhance your geometry skills and problem-solving abilities.

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The Midsegment Theorem

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  1. The Midsegment Theorem Goal 1 Using Midsegments of Triangles. Goal 2 Using Properties of Midsegments.

  2. 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 is half as long.

  3. Using Midsegments of a Triangle a) In XYZ, which segment is parallel to b) Find YZ and XY

  4. Quick Check: Find the m<VUZ. X 65O U Z Y V

  5. Example 1 Identifying Parallel Segments • What are the three pairs of parallel segments in triangle DEF? • RS || ____ • ST || ____ • TR || ____

  6. Example 2 In the diagram, ST and TU are midsegments of triangle PQR. Find PR and TU. 5 ft 16 ft TU = ________ PR = ________

  7. Example 3 In the diagram, XZ and ZY are midsegments of triangle LMN. Find MN and ZY. 14 cm 53 cm ZY = ________ MN = ________

  8. Example 4 Finding Lengths • In triangle QRS, • T, U, and B are midpoints. • What are the lengths of TU, UB, and QR?

  9. Example 5 Using Midsegments of a Triangle Find JK and AB 12 5 JK = ________ AB = ________

  10. 52 3x- 4 Example 6 In the diagram, ED and DF are midsegments of triangle ABC. Find the value of x and DF. x = ________ 10 DF = ________ 26

  11. Example 7 Given: DE = x + 2; BC = Find the value of x and DE. x + 2

  12. Example 7 are midsegments in XYZ. Find the perimeter of XYZ.

  13. Example 8 Given: X, Y, and Z are the midpoints of AB, BC, and AC respectively. AX = 2; XY = 3; BC = 9 Find the perimeter of ABC. (it’s a decimal)

  14. 5-1 Daily Quiz 12/1 In XYZ, M, N and P are the midpoints. The Perimeter of MNP is 64. a) Find NP. b) Find perimeter of XYZ a) NP + MN + MP = 64 (Definition of Perimeter) NP + + = 64 NP + = 64 NP = b) P = XY + YZ + ZX P = ___ + ___ + ____ P = ______ x 24 M P 22 Y Z N

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