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:

Step1: Identify midpoints

X (mid FG), Y (mid GH), Z (mid FH) in equilateral △FGH.

Step2: Coordinates setup

Let F(0,0), H(s,0), G(s/2, (s√3)/2). X(s/4, (s√3)/4), Y(3s/4, (s√3)/4).

Step3: Check parallelism

XY slope=0, FH slope=0 ⇒ XY||FH. FX slope=√3, YH slope=-√3 ⇒ not parallel.

Step4: Classify quadrilateral

Only one pair of parallel sides (XY||FH).

Answer:

C. trapezoid