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. In triangle (FGH), (ST) is a mid - segment since (S) is the midpoint of (GH) and (T) is the midpoint of (HF).

Step2: Analyze the relationship between (ST) and (GF)

By the mid - segment theorem, (ST=\frac{1}{2}GF). We are given that (ST = 8\mathrm{cm}).

Step3: Solve for (GF)

If (ST=\frac{1}{2}GF), then (GF = 2\times ST). Substituting (ST = 8\mathrm{cm}), we get (GF=2\times8\mathrm{cm}=16\mathrm{cm}).

Answer:

(16\mathrm{cm})