Since E is the midpoint of TU and H is the midpoint of TV, then segment EH is parallel to UV and its length is half of UV's length.
Therefore, the length of segment EH is 80 / 2 = <<80/2=40>>40. Answer: \boxed{40}.
Find the length of segment HE. Points E, D, and H are the midpoints of the sides of triangle TUV. UV = 80, TV = 100, and HD = 80
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