Question

Points S and T are midpoints of the sides of triangle FGH.Triangle G H F is cut by line segment S T. Point S is the midpoint of side H G and point T is the midpoint of H F. The lengths of H T and T F are 6 centimeters. The lengths of H S and S G are 4 centimeters. The length of S T is 8 centimeters.What is GF?

Answer 1

The measure of length of GF is 16 cm.

Given that point S is the midpoint of side HG and point T is the midpoint of HF of triangle FGH, the line segment ST is parallel to the side GF, and the triangles FGH and TSH are similar with proportional sides, then:

$\frac{GF}{ST}=\frac{FH}{TH}=\frac{GH}{SH}$

We are given the following;

FH = HT + FT = 6 + 6 = 12 cm [HT = FT = 6 cm]

GH = HS + GS = 4 + 4 = 8 cm [HS = GS = 4 cm]

ST = 8 cm

Substitute the given values, we will get the following;

$\frac{GF}{8} =\frac {12}{6} = \frac{8}{4}\\\frac{GF}{8} =\frac {12}{6}\\\frac{GF}{8} = 2$

GF = 2 * 8 = 16 cm

Thus, the measure of the length of GF is 16 cm.

To learn more about the midpoint theorem visit:

brainly.com/question/16958177

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