Yes 1 of the diagonals of a kite is symmetrical
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The quadrilateral you are referring to is called a kite. A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length, and one pair of diagonals that are not equal in length. Additionally, a kite has two axes of symmetry, which are lines that divide the kite into two congruent halves.
a hexagon has 4 axes ofsymmetry.
No, the diagonals are not equal.
Yes the diagonals of a kite bisect each other at 90 degrees.
Only when the rectangle is a square.