Question

points e, d, and h are the midpoints of the sides of \\( \triangle tuv \\). \\( uv = 106 \\), \\( tv = 128 \\), and \\( hd = 106 \\). find he.
\\( he = \square \\)

Explanation:

Step1: Recall the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the mid - points of two sides) is parallel to the third side and half of its length.

Step2: Identify the relevant mid - segment

Since \(E\) and \(H\) are mid - points, \(HE\) is a mid - segment. \(HE\) is parallel to \(UV\) and \(HE=\frac{1}{2}TV\) (by the mid - segment theorem).

Step3: Calculate the value of \(HE\)

Given \(TV = 128\). Substitute \(TV\) into the formula \(HE=\frac{1}{2}TV\). So \(HE=\frac{1}{2}\times128 = 64\).

Answer:

64