Question

analyze the diagram. which quadrilateral is a kite?

Explanation:

Step1: Recall the definition of a kite

A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length.

Step2: Analyze the first diagram

In the first diagram, quadrilateral \(ABCD\) has \(AB = BC\) and \(AD = DC\), which are two distinct pairs of adjacent sides equal.

Step3: Analyze the second diagram

In the second diagram, quadrilateral \(MNOP\) has \(MN = NP\) but the other pair of adjacent sides \(MO\) and \(OP\) are not equal to \(MN\) and \(NP\) in the adjacent - side sense (the non - adjacent side \(OP\) is marked as equal to a non - adjacent side in a non - kite - like structure).

Step4: Analyze the third diagram

In the third diagram, quadrilateral \(MNPO\) has only one pair of adjacent sides (\(MN = NP\)) equal, and the other sides do not form a second distinct pair of adjacent equal sides.

Answer:

The first quadrilateral (the one with vertices \(A\), \(B\), \(C\), \(D\)) is a kite.