The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .Which statement correctly describes whether quadrilateral DEFG is a rhombus? Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length. Quadrilateral DEFG is not a rhombus because there is only one pair of opposite sides that are parallel. Quadrilateral DEFG is not a rhombus because opposite sides are parallel but the four sides do not all have the same length. Quadrilateral DEFG is not a rhombus because there are no pairs of parallel sides.
Accepted Solution
A:
Quadrilateral DEFG with coordinates of vertices of D(-2,5), E(2,4) , F(0,0) , and G(-4,1) is indeed a rhombus because it has opposite sides that are parallel, and all four sides are of the same length. This also means that the quadrilateral has equal opposite obtuse angles and equal opposite acute angles.