The Midsegment Theorem

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Presentation transcript:

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

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.

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

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

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

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

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

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

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

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

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

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

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)

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