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: Use the mid - segment theorem

The mid - segment theorem states that 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 \(ON=\frac{1}{2}DF\). Given \(ON = 38\mathrm{cm}\), then \(DF=2\times ON\).

Step2: Calculate \(DF\)

Since \(ON = 38\mathrm{cm}\), \(DF = 2\times38=76\mathrm{cm}\).

Step3: Use the property of midpoint \(M\)

Since \(M\) is the midpoint of \(DF\), then \(DM=\frac{1}{2}DF\).

Step4: Calculate \(DM\)

Substitute \(DF = 76\mathrm{cm}\) into the formula \(DM=\frac{1}{2}DF\). So \(DM=\frac{76}{2}=38\mathrm{cm}\).

Answer:

\(38\mathrm{cm}\)