Question

points o and n are midpoints of the sides of triangle def. what is dm? 22 cm 30 cm 38 cm 76 cm

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is parallel to the third side and half its length. Here, \(ON\) is a mid - segment of \(\triangle DEF\). So, \(ON=\frac{1}{2}DF\).

Step2: Find the length of \(DF\)

Since \(ON = 38\) cm and \(ON=\frac{1}{2}DF\), then \(DF=2\times ON\). Substituting the value of \(ON\), we get \(DF = 2\times38=76\) cm.

Step3: Use the property of a midpoint

Since \(M\) is the midpoint of \(DF\) (given that \(O\) and \(N\) are midpoints and by the construction of the triangle mid - segments and mid - points), then \(DM=\frac{1}{2}DF\).
Substituting \(DF = 76\) cm, we have \(DM=\frac{76}{2}=38\) cm.

Answer:

\(38\) cm