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A square and a rhombus
A square is on example. The perpendicular bisectors of the sides and the two diagonals comprie four lines of symmetry.
The best classification for a parallelogram that has perpendicular diagonals is a rhombus. A rhombus has four sides that are congruent. The also diagonals bisect the vertex angles of this type of parallelogram.
It is not possible to have five perpendicular sides; four or eight, but not five. A shape with five equal sides is a pentagon.
You are a square
It is a rhombus. All four sides have the same length and the diagonals are therefore perpendicular.
A square and a rhombus
A square is on example. The perpendicular bisectors of the sides and the two diagonals comprie four lines of symmetry.
The diagonals of a rhombus are perpendicular. A rhombus is a special kind of parallelogram. It has the characteristics of a parallelogram (both pairs of opposite sides parallel, opposite sides are congruent, opposite angles are congruent, diagonals bisect each other.) It also has special characteristics. It has four congruent sides. So it looks like a lopsided or squished square. Its diagonals are perpendicular. Another property: each diagonal bisects two angles of the rhombus.
The best classification for a parallelogram that has perpendicular diagonals is a rhombus. A rhombus has four sides that are congruent. The also diagonals bisect the vertex angles of this type of parallelogram.
It is not possible to have five perpendicular sides; four or eight, but not five. A shape with five equal sides is a pentagon.
You are a square
"It has four sides" is a description that does not guarantee that a quadrilateral is a square.
a quadrilateral is a shape with four equal sides.
Check to see that -- it has four sides -- its two diagonals are equal.
It is a rhombus
A kite would fit the given description.