which statement proves that quadrilateral jklm is a kite?

$\angle m$ is a right angle and $\overline{mk}$ bisects $\angle lmj$.
$lm = jm = 3$ and $jk = lk = \sqrt{17}$.
$\overline{mk}$ intersects $\overline{lj}$ at its midpoint.
the slope of $\overline{mk}$ is $-1$ and the slope of $\overline{lj}$ is $1$.

Question

which statement proves that quadrilateral jklm is a kite?

$\angle m$ is a right angle and $\overline{mk}$ bisects $\angle lmj$.
$lm = jm = 3$ and $jk = lk = \sqrt{17}$.
$\overline{mk}$ intersects $\overline{lj}$ at its midpoint.
the slope of $\overline{mk}$ is $-1$ and the slope of $\overline{lj}$ is $1$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Kite Properties" ], "new_concepts": [], "current_concepts": [ "Kite Properties", "Distance Formula", "Coordinate Geometry" ] } ## Define the definition of a kite Using the *Kite Properties* knowledge point A kite is a quadrilateral with two distinct pairs of adjacent congruent sides. ## Calculate the lengths of the adjacent sides Using the *Kite Properties* knowledge point $$ \begin{aligned} &LM = \sqrt{(1-1)^2 + (5-2)^2} = \sqrt{0 + 9} = 3\ &JM = \sqrt{(4-1)^2 + (5-5)^2} = \sqrt{9 + 0} = 3\ &JK = \sqrt{(5-4)^2 + (1-5)^2} = \sqrt{1 + 16} = \sqrt{17}\ &LK = \sqrt{(5-1)^2 + (1-2)^2} = \sqrt{16 + 1} = \sqrt{17} \end{aligned} $$ ## Match with the definition of a kite Using the *Kite Properties* knowledge point $$ \begin{aligned} &LM = JM = 3\ &JK = LK = \sqrt{17} \end{aligned} $$ This shows two distinct pairs of adjacent congruent sides, proving $JKLM$ is a kite.

(A) $\angle M$ is a right angle and $\overline{MK}$ bisects $\angle LMJ$.

(B) $LM = JM = 3$ and $JK = LK = \sqrt{17}$.

(C) $\overline{MK}$ intersects $\overline{LJ}$ at its midpoint.

(D) The slope of $\overline{MK}$ is $-1$ and the slope of $\overline{LJ}$ is $1$.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Kite Properties" ] }

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Explanation:

Define the definition of a kite

Calculate the lengths of the adjacent sides

Match with the definition of a kite

Answer: