Question

a quadrilateral abcd has diagonals that are perpendicular bisectors of one another. which of the following classifications must apply to quadrilateral abcd? i. parallelogram ii. rhombus iii. square

Explanation:

• For parallelogram: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Here, the diagonals are perpendicular bisectors of one another. The property of diagonals bisecting each other is a key property of parallelograms.
• For rhombus: A rhombus is a parallelogram with perpendicular diagonals. Since we have already established it is a parallelogram (from the bisecting diagonals property) and the diagonals are perpendicular, it must be a rhombus.
• For square: A square is a special - case of a rhombus where the diagonals are not only perpendicular bisectors but also equal in length. We are not given any information about the lengths of the diagonals. So, we cannot conclude it is a square.

Answer:

I. parallelogram, II. rhombus