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. 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:

\(16\mathrm{cm}\)