Question

points e, d, and h are the midpoints of the sides of \\( \delta tuv \\). \\( uv = 88 \\), \\( tv = 108 \\), and \\( hd = 88 \\). find tu.

\\( tu= \\)

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. Here, since \(E\), \(D\), and \(H\) are midpoints, \(HD\) is a mid - segment. If \(HD\) is parallel to \(TU\), then \(TU = 2\times HD\).

Step2: Calculate the length of \(TU\)

Given \(HD = 88\), using the formula \(TU=2\times HD\), we substitute \(HD = 88\) into the formula. So \(TU = 2\times88=176\).

Answer:

176