Question

given only the information in the image, what is the best description of quadrilateral luck?
parallelogram
rhombus
quadrilateral
kite
ky = yu
lk = lu
m∠lyu = 90°

Explanation:

Step1: Recall kite - properties

A kite has two pairs of adjacent sides equal. Here $\overline{LK}=\overline{LU}$ which is one pair of adjacent equal - sides. Also, a kite has diagonals that are perpendicular to each other. Given $m\angle LYU = 90^{\circ}$, the diagonals $\overline{LC}$ and $\overline{KU}$ are perpendicular. And $\overline{KY}=\overline{YU}$ shows that one diagonal ($\overline{LC}$) bisects the other diagonal ($\overline{KU}$). These are all properties of a kite.

Step2: Analyze other options

A parallelogram has opposite sides equal and parallel, which is not indicated here. A rhombus has all four sides equal, which is not the case as we only know one pair of adjacent sides are equal. Just calling it a quadrilateral is too general when more specific properties are given to identify it as a kite.

Answer:

D. Kite