Points E, D, and H are the midpoints of the sides of TUV. UV=112, TV=140, and HD=112. Find HE.
Since E, D, and H are the midpoints of the sides of triangle TUV, we know that the lengths of lines TE and EU are equal to the lengths of lines TV and VU respectively, and the lengths of lines HD, DH are equal to the lengths of lines TU, and UV respectively.
Therefore, TE = TV = 140, EU = VU = 112, and HD = TU = 112.
Since E and H are midpoints of TV and TU respectively, EH is parallel to VT, and the lengths of VT and HE are equal.
Since EH is parallel to VT, and the lengths of VT and VU are equal, we can conclude that EH is also parallel to VU.
Therefore, the lengths of VT and HE are equal to the lengths of VU and EU respectively.
Therefore, VT = VU = 112, and HE = EU = 112.
Therefore, the length of HE is 112.