No because a kite is a 4 sided quadrilateral with two diagonals of different lengths that intersect each other at right angles.
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Not necessarly. If the sum of two of the sides congruent to each other are greater than that of the sides opposite them, then no. If however the kite forms a rombus ot square, the diagnoles will form four congruent triangles with the base of both being the line of symmetry.
square
square
Any regular polygon. Lots of irregular polygons can also have congruent diagonals, for example a kite. The answer should not be "a square" because it is a rectangle - a special case but a rectangle nevertheless.
A kite has two pairs of adjacent sides congruent. The diagonals intersect at right angles and bisect one set of angles.