Question

choose all answers that describe the quadrilateral ijkl if diagonal (overline{ik}) bisects diagonal (overline{jl}), (overline{jl}) bisects (overline{ik}), and (overline{ik}perpoverline{jl}).
answer attempt 1 out of 2
parallelogram
rectangle
rhombus
square
trapezoid

Explanation:

Step1: Recall properties of quadrilaterals

• Parallelogram: Diagonals bisect each other. But in a general parallelogram, diagonals are not perpendicular.
• Rectangle: Diagonals are equal and bisect each other. Diagonals are not perpendicular in a general rectangle.
• Rhombus: Diagonals bisect each other at right - angles.
• Square: A special case of a rhombus (and rectangle). Diagonals bisect each other at right - angles.
• Trapezoid: Diagonals do not bisect each other in a general trapezoid.

Step2: Check the given condition

The condition is that one diagonal bisects the other and they are perpendicular. Rhombus (and square which is a special rhombus) satisfy the property that diagonals bisect each other at right - angles.

Answer:

Rhombus, Square