Question

points s and t are midpoints of the sides of triangle fgh. what is gf? 4 cm 6 cm 8 cm 16 cm

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length. Here, \(ST\) is a mid - segment of \(\triangle FGH\).

Step2: Use the property of mid - segment

Since \(ST\) is a mid - segment and \(ST = 8\mathrm{cm}\), and \(GF\) is the side parallel to \(ST\). By the mid - segment theorem, if \(ST=\frac{1}{2}GF\), then \(GF = 2\times ST\).
Substitute \(ST = 8\mathrm{cm}\) into the formula \(GF = 2\times ST\).
\(GF=2\times8\mathrm{cm}\)

Answer:

\(16\mathrm{cm}\) (the fourth option)