Question

points e, d, and h are the midpoints of the sides of \\( \triangle tuv \\). \\( uv = 92, tv = 114 \\), and \\( hd = 92 \\). find tu.

\\( tu = \square \\)

Explanation:

Step1: Recall 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. In \(\triangle TUV\), since \(H\) is the midpoint of \(TV\) and \(D\) is the midpoint of \(VU\), then \(HD\) is a mid - segment.

Step2: Apply the mid - segment formula

If \(HD\) is a mid - segment of \(\triangle TUV\) with respect to side \(TU\), then \(HD=\frac{1}{2}TU\).
We are given that \(HD = 92\). Substituting \(HD\) into the formula \(TU = 2\times HD\).

$$TU=2\times92$$

Answer:

\(184\)