1. 5.1 Midsegments of Triangles

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

3. 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

4. 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.

6. 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.

8. 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.