The a) AB segment is parallel to FE . Therefore , a) AB is correct.
The concept of midsegments in triangles provides a clear rationale for concluding that segment AB is parallel to side FE in the given scenario.
In geometry, a midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle.
The midpoint of a line segment divides it into two equal parts.
Applying this concept to the triangle in question, where AB is the midsegment, it implies that AB connects the midpoints of sides AC and BC.
The statement correctly notes that AB passes through the midpoint of side AC.
According to the midsegment theorem, the midsegment of a triangle is parallel to the third side of the triangle and is half its length.
In this case, since AB is the midsegment connecting the midpoints of sides AC and BC, it is parallel to side AC.
This conclusion arises from the geometric property that midsegments, by definition, are parallel to one side of the triangle and pass through the midpoint of that side.
Therefore, based on the principles of midsegments in triangles, it can be confidently asserted that AB is parallel to side FE in the given context.