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

Answer 1

Quadrilateral FXYH is shape of trapezoid.

Explanation:

Given : Triangle FGH is equilateral. The midpoints of the sides are connected to form triangle XYZ. Line segment XY is parallel to line segment FH.

To find : What type of figure is quadrilateral FXYH.

Solution : We have given that a triangle FGH is equilateral. We will take triangle base FH .

Now, we will mark mid points of all sides of triangle FGH as XYZ.

Here, X is mid point of FG and Y is mid point of GH and Z is mid point of FH.

Joint the points XYZ , we can line XY is parllel to FH .

We can see FXYH is shape of trapezoid.

Therefore, quadrilateral FXYH is shape of trapezoid.

Answer 2

If triangle FGH is equilateral, then all its sides are congruent. The midpoints of the sides are connected to form triangle XYZ. Lines XY, YZ and XZ are middle lines of the triangle FGH.

Triangle midpoint theorem: 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.

According to this theorem, the segment XY is parallel to the side FH and its length is half of FH length.

Therefore, quadrilateral FXYH is trapezoid with two parallel bases XY and FH.

Answer: correct choice is C