Question

points e, d, and h are the midpoints of the sides of \\( \triangle tuv \\). \\( uv = 48 \\), \\( tv = 80 \\), and \\( hd = 48 \\). find \\( he \\).

Explanation:

Step1: Use 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.
Since \(E\) and \(H\) are midpoints of \(TU\) and \(TV\) respectively, \(HE\) is a mid - segment of \(\triangle TUV\) parallel to \(UV\).

Step2: Calculate the length of \(HE\)

By the mid - segment theorem, \(HE=\frac{1}{2}UV\)
Given \(UV = 48\), then \(HE=\frac{1}{2}\times48\)

Answer:

\(24\)