Question

In the diagram below of triangle CDE,F is the midpoint of CE and G is the midpoint of DE. If FG = -2x +10, and CD p -7x + 29, what is the measure of FG?

Answer 1

The value of FG is 4

The Midpoint Theorem states that in a triangle, a line segment connecting the midpoints of two sides is parallel to the third side and is half its length.

This theorem highlights a relationship involving midpoints and parallel lines within triangles.

In triangle CDE,

F is the midpoint of CE and G is the midpoint of DE.

This means that CD is the third side that will be parallel to FG.

Therefore,

CD = 2 FG

-7x + 29 = 2( -2x + 10)

-7x + 29 = -4x + 20

-3x = -9

x = -9/-3

x = 3

Therefore;

FG = -2(3) + 10

FG = -6 + 10

FG = 4