Question

which of the following quadrilaterals have diagonals that are always perpendicular to each other? check all that apply.

a. square
b. rectangle
c. parallelogram
d. rhombus

Explanation:

Analyze the properties of a Rhombus

Using the Diagonals of a Rhombus and Rhombus Properties knowledge points

• A rhombus is defined as a parallelogram with four congruent sides.
• A key theorem states that the diagonals of a rhombus are always perpendicular to each other.

Analyze the properties of a Square

Using the Rhombus Properties knowledge point

• A square is a regular quadrilateral, meaning it is both a rectangle (four right angles) and a rhombus (four congruent sides).
• Since a square is a type of rhombus, it inherits all properties of a rhombus, including having perpendicular diagonals.

Analyze the properties of a Rectangle

Using the Properties of Rectangles knowledge point

• A rectangle is a parallelogram with four right angles.
• Its diagonals are congruent, but they are only perpendicular if the rectangle is also a square. Thus, they are not always perpendicular.

Analyze the properties of a Parallelogram

• A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
• Its diagonals bisect each other, but they are only perpendicular if the parallelogram is a rhombus or a square. Thus, they are not always perpendicular.

Answer:

• A. Square (Correct answer)
• B. Rectangle
• C. Parallelogram
• D. Rhombus (Correct answer)