Question

which statement proves that quadrilateral jklm is a kite?
∠m is a right - angle and mk bisects ∠lmj.
lm = jm = 3 and jk = lk=sqrt{17}
the slope of mk is - 1 and the slope of lj is 1

Explanation:

Step1: Recall kite - definition

A kite is a quadrilateral with two pairs of adjacent sides equal.

Step2: Analyze each option

• Option 1: Just having a right - angle and a bisector does not guarantee it's a kite.
• Option 2: If \(LM = JM=3\) and \(JK = LK=\sqrt{17}\), we have two pairs of adjacent sides equal. This satisfies the definition of a kite.
• Option 3: Just knowing the slopes of the diagonals being negative reciprocals only shows that the diagonals are perpendicular, which is a property of a kite but not sufficient to prove it's a kite on its own.

Answer:

LM = JM = 3 and JK = LK = √17