Question

1. if the diagonals of a parallelogram are perpendicular and not congruent, which of the following best describes the parallelogram? a rectangle a square an isosceles trapezoid a rhombus

Explanation:

Step1: Recall properties of each shape

• Rectangle: Diagonals are congruent (equal in length) and bisect each other.
• Square: Diagonals are congruent, perpendicular, and bisect each other.
• Isosceles trapezoid: Not a parallelogram. Diagonals are congruent.
• Rhombus: Diagonals are perpendicular bisectors of each other. In a rhombus, diagonals are not congruent (unless it is a square).

Step2: Match with given condition

The problem states that diagonals of a parallelogram are perpendicular and not congruent.

• Since it is a parallelogram, we can rule out isosceles trapezoid (not a parallelogram).
• Rectangle has congruent diagonals, so it is ruled out.
• Square has congruent diagonals, so it is ruled out.
• Rhombus (a type of parallelogram) has perpendicular diagonals and non - congruent diagonals (in general, unless it is a square, but the problem says diagonals are not congruent).

Answer:

A rhombus