a kite
/ kyt /
Think of the toy kite you fly on a string: a four-sided figure with two short sides meeting at the top and two longer sides meeting at the bottom, the whole shape mirror-symmetric down the middle. That symmetric, arrowhead-or-diamond outline is a kite in geometry.
Precisely, a kite is a quadrilateral with two distinct pairs of equal-length sides that are adjacent (consecutive), rather than opposite. So the sides come as two pairs sharing a vertex — say AB = AD and CB = CD — not as opposite matching pairs (which would make a parallelogram). From this follow the kite's signature properties: the diagonals are perpendicular to each other; the diagonal joining the two 'apex' vertices (where unequal pairs meet) is the axis of symmetry and bisects the other diagonal; and exactly one pair of opposite angles, the two between the unequal sides, are equal. A kite also has an inscribed circle touching all four sides.
The kite branches off the quadrilateral hierarchy in its own direction — it is generally not a parallelogram, since its equal sides are adjacent, not opposite. It overlaps the parallelogram family only at the rhombus: a kite with all four sides equal is a rhombus (and then both diagonals bisect each other). The subtlety to watch: a concave 'dart' or arrowhead with two pairs of adjacent equal sides is sometimes also called a kite (a non-convex kite); the convex kite is the familiar flying-kite shape, and many textbooks restrict 'kite' to the convex case, so check the convention.
In kite ABCD with AB = AD = 3 and CB = CD = 5, the diagonal AC is the axis of symmetry: it is perpendicular to BD and bisects BD, while BD does not bisect AC. The angles at B and D (between the unequal sides) are equal to each other.
One diagonal of a kite is an axis of symmetry that perpendicularly bisects the other.
A kite's equal sides are adjacent, not opposite, so a kite is generally not a parallelogram; the two families meet only at the rhombus (a kite with all sides equal).