Question

Show that DEFG is a rectangle.

Answer 1

in the steps

Explanation:

D(-2,3) E(4,-1) F(2,-4) G(-4,0)

slope DG: (0-3)/(-4+2) = -3/-2 = 3/2

slope EF: (-4+1)/(2-4) = -3/-2 = 3/2

DG // EF

slope DE: (-1-3)/(4+2) = -4/6 = -2/3

slope GF: (-4-0)/(2+4) = -4/6 = -2/3

DE // GF

slope DG = - 1/slope DE

DG ⊥ DE

The same reason

DG ⊥ GF

DE ⊥ EF

EF ⊥ GF

∴ DEFG is a parallelogram with four 90° interior angles, it's a rectangle

Answer 2

opposite sides that are parallel,

opposite angles that are congruent,

opposite sides that are congruent,

consecutive angles that are supplementary, and

diagonals that bisect each other.

Explanation:

not sure if this is the kind of answer you're looking for so i'm sorry if this didn't help