Points E, D, and H are the midpoints of the sides of TUV. UV=96, TV=116, and HD=96. Find TU.
To find TU, we can use the midpoint theorem. The midpoint theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length.
Given that points E, D, and H are the midpoints of the sides of triangle TUV, we can deduce the following:
1. ED is parallel to TU and half its length.
2. HD is parallel to TV and half its length.
Since HD is parallel to TV, and HD = 96, we can conclude that TV = 2 * HD = 2 * 96 = 192.
Now let's apply the midpoint theorem again:
ED is parallel to TU and half its length. Hence, TU = 2 * ED.
To determine ED, we need more information. Specifically, we need to know either the length of UV or the length of TV. In this case, we are given that UV = 96. Since UV is not needed to find TU or is it a missing side, we can conclude that it is not necessary to determine TU.
Therefore, the length of TU cannot be determined with the given information.