Yes but not at right angles
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The following are all bisected by the diagonal of a square:The corner anglesThe surface of the squareThe other diagonal
They are perpendicular and one diagonal is bisected.
Any angle can be bisected using a compass and a straight edge.
The diagonals are perpendicular to one another. The shorter diagonal is bisected by the longer diagonal. The kite is symmetrical about the longer diagonal. The longer diagonal bisects the angles at each end of the diagonal.
A 9 x 12 rectangle has a diagonal of 15.