5.1 Midsegments of Triangles

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Presentation transcript:

5.1 Midsegments of Triangles

Midsegment of a Triangle – -The segment connecting the midpoints of two sides of the triangle. Midpoint Midsegment Midpoint

Theorem The segment that joins the midpoints of two sides of a triangle. (1) is parallel to the third side. (2) is half as long as the third side. C D B A E

Some Examples Y M X T Z N M, N, and T are midpoints If XZ = 10, then MN = _____ If TN = 7, then XY = _____ If ZN = 8, then TM = _____ If XY = k, then TN = _____ Suppose XY =10, YZ =14, and XZ= 8, find the lengths of the sides of triangle MNT.

Assuming that D, E, and F are midpoints, find all segment lengths. C B A 12 8 12 10 Assuming that D, E, and F are midpoints, find all segment lengths.

Find x, y, and z, and each segment length. 3z2-2y 8x-12 2x+16 5y-10 3y+10 2z2+.5y D E B C Find x, y, and z, and each segment length.