Short Answer 
A kite is a quadrilateral with two pairs of congruent sides that do not share endpoints. Its diagonals intersect at right angles, with one bisecting the other, and the angles at the ends of the cross diagonal are congruent, ensuring its unique symmetrical properties.
Step 1: Understand the Properties of a Kite
A kite is a specific type of quadrilateral that features two pairs of consecutive sides that are congruent. This means that in a kite, there are two sets of sides where each pair is equal in length. Importantly, the sides in each pair must be disjoint, meaning they do not share any endpoints. For example, in kite QPQR, we can state that QP is congruent to QR, but QR must not be congruent to RS.
Step 2: Analyze the Diagonals of the Kite
The diagonals of a kite intersect in such a way that one diagonal bisects the other at a right angle. In this case, if PM and MR are the diagonals, we have PM congruent to MR. This property is crucial as it helps to define the shape’s symmetry and ensures that the angles opposite the longer diagonal are congruent.
Step 3: Verify the Angles and Their Relationships
In a kite, the angles located at the endpoints of the cross diagonal must also be congruent. This means that the angles ‚a†QPS and ‚a†QRS are equal. By confirming that these relationships hold true‚AiQP congruent to QR, PM congruent to MR, and ‚a†QPS congruent to ‚a†QRS‚Aia kite structure is validated. This symmetry underlies the unique properties that distinguish kites from other types of quadrilaterals.