Question

if lk = 58, what is nm? nm = (simplify your answer.)

Explanation:

Step1: Recall the mid - segment theorem

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

Step2: Analyze the given triangle

Since \(N\) is the mid - point of \(LJ\) (three marks on \(LN\) and \(NJ\)), \(O\) is the mid - point of \(LK\) (two marks on \(LO\) and \(OK\)), and \(M\) is the mid - point of \(JK\) (one mark on \(JM\) and \(MK\)). In \(\triangle LJK\), \(NO\) is a mid - segment. Also, in \(\triangle NJM\) and other sub - triangles, we can use the mid - segment property. Another way: The figure formed by \(N\), \(O\), \(M\) is such that \(NM\) is related to \(LK\). By the mid - segment theorem (or the property of a triangle with mid - points), \(NM=\frac{1}{2}LK\)

Step3: Substitute the value of \(LK\)

Given \(LK = 58\), then \(NM=\frac{1}{2}\times58\)
$$NM = 29$$

Answer:

\(29\)