Points E,D, and H are the midpoints of the sides of triangle TUV. UV = 82, TV = 106 and HD = 82
If E, D, and H are the midpoints of the sides of triangle TUV, then the segment EH is parallel to the side UV and equal in length to half of the side UV.
Since HD = 82 and EH is parallel to UV,
HD = EH
Therefore, EH = 82.
Also, since EH is parallel to UV and EH = 82,
UV = 2 * EH = 2 * 82 = 164.
Similarly, if D is the midpoint of TV and EH is parallel to TV, then DH = EH.
Therefore, DH = 82.
Since DE is parallel to TV and DH = 82,
TV = DE + EH + DH = EH + DH + DE = 82 + 82 + DE = 164 + DE.
Given that TV = 106,
106 = 164 + DE.
DE = 106 - 164.
DE = -58.
Therefore, DE = -58.
In triangle TUV, UV = 82, TV = 106, DE = -58.