What is GE ?
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GE= 10 units

Step-by-step explanation:

The line segment connecting the midpoints of  two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

As given,

EX = XF, so X is the mid point of EF

GY = YF, so Y is the mid point of GF

Hence, XY is the line segment connecting the midpoints of two sides of a triangle.

Applying the mid-point theorem,

GE = 2XY = 2×5 = 10 units

The length of GE is 10 units

Explanation:

Given that the length of XY = 5 units and YZ = 4.6 units

The length of GE:

We need to determine the length of GE

From the figure, we can see that ZY bisects GE and XY bisects EF.

The lines ZY and XY both bisect GF.

The midpoint theorem states that "the line segment connecting the midpoints of  two sides of a triangle is parallel to the third side and is congruent to one half of the third side".

Since, we have,

EX = XF and X is the midpoint of EF

GY = YF and Y is the midpoint of GF

Since, XY is the line segment that connects the midpoints of the two sides of the triangle.

Applying the midpoint theorem, we have,

Thus, the length of GE is 10 units.