A square, a rhombus and a kite all have diagonals that are perpendicular and meet each other at right angles.
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Yes
Square, rhombus and a kite
Yes, the diagonals of a square are congruent (equal in length) and are perpendicular.
In most shapes the diagonals do not bisect one another. It might be possible to answer the question if it were more specific. To start with, shapes with how many sides?
All quadrilaterals (four sided shapes) have 2 diagonals.