Which statement proves that quadrilateral jklm is a kite?
a. ∠m is a right angle and mk bisects ∠lmj.
b. lm = jm = 3 and jk = lk = √17.
c. mk intersects lj at its midpoint.
d. the slope of mk is –1 and the slope of lj is 1.

A quadrilateral is a kite if the diagonals are:

i) perpendicular
ii) bisect each other
iii) not equal ( together with conditions i and ii this would make the quadrilateral a square)

Another definition of the kite is :

a quadrilateral with 2 pairs of equal adjacent sides.

Let's check the choices one by one:

A. ∠M is a right angle and MK bisects ∠LMJ.

according to these, ML and MJ may well be not equal...

B. LM = JM = 3 and JK = LK = √17.

this makes the quadrilateral a kite.

C. MK intersects LJ at its midpoint

if they are not perpendicular, the quadrilateral is not a kite.

D. The slope of MK is –1 and the slope of LJ is 1.

this only means that MK and LJ are perpendicular, but not whether they bisect each other,

only B