Question

points e, d, and h are the midpoints of the sides of \\( \triangle tuv \\). \\( uv = 46 \\), \\( tv = 58 \\), and \\( hd = 46 \\). find he.

\\( he = \square \\)

Explanation:

Step1: Use the mid - segment theorem

Since \(E\), \(D\), and \(H\) are mid - points of the sides of \(\triangle TUV\), \(HE\) is parallel to \(UV\) and \(HE=\frac{1}{2}UV\) (by the mid - segment theorem of a triangle which states that the segment connecting the mid - points of two sides of a triangle is parallel to the third side and half its length).

Step2: Substitute the value of \(UV\)

Given \(UV = 46\). Then \(HE=\frac{1}{2}\times46\).

Answer:

\(23\)