Question

points e, d, and h are the midpoints of the sides of \\( \triangle tuv \\). \\( uv = 104 \\), \\( tv = 132 \\), and \\( hd = 104 \\). find he.

\\( he = \square \\)

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length.

Step2: Identify the mid - segment

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

Step3: Apply the mid - segment formula

By the mid - segment theorem, \(HE=\frac{1}{2}UV\).

Step4: Substitute the value of \(UV\)

Given \(UV = 104\), then \(HE=\frac{1}{2}\times104 = 52\).

Answer:

\(52\)