We can tell that the slopes of the opposite sides of our quadrilateral are not equal. Therefore, both pairs of opposite sides are not parallel and our quadrilateral can be a kite. To check, we can find the lengths of its sides using the Distance Formula.
Side
Distance Formula
Simplified
Length of FG: ( 0,0), ( 5,5)
sqrt(( 5- 0)^2+( 5- 0)^2)
sqrt(50)
Length of GH: ( 5,5), ( 8, 4)
sqrt(( 8- 5)^2+( 4- 5)^2)
sqrt(10)
Length of HI: ( 8,4), ( 7, 1)
sqrt(( 7- 8)^2+( 1- 4)^2)
sqrt(10)
Length of IF: ( 7, 1), ( 0,0)
sqrt(( 0- 7)^2+( 0- 1)^2)
sqrt(50)
Our quadrilateral has two congruent pairs of consecutive sides, and its opposite sides are not congruent. Therefore, the most precise name for this quadrilateral is kite.
