Question

triangle fgh is equilateral. the midpoints of the sides are connected to form triangle xyz. line segment xy is parallel to line segment fh. what type of figure is quadrilateral fxyh? kite rhombus trapezoid parallelogram

Explanation:

A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. In quadrilateral \( FXYH \), since \( XY\parallel FH \) (given that \( XY \) is part of the triangle formed by connecting mid - points and the property of mid - segment in a triangle), and there is no information to suggest the other pair of sides (\( FX \) and \( YH \)) are parallel. A kite has two pairs of adjacent equal sides, a rhombus has all sides equal and both pairs of opposite sides parallel, and a parallelogram has both pairs of opposite sides parallel. Since only one pair of sides (\( XY\) and \( FH\)) is parallel, it fits the definition of a trapezoid.

Answer:

trapezoid