Question

classify the following properties by the most specific shape they apply to.
options (7)
diagonals are congruent
diagonals bisect each other
only 1 pair of parallel sides
diagonals are perpendicular
4 congruent sides
exactly 2 pairs of parallel sides
4 right angles

parallelogram
trapezoid
rhombus
rectangle

Explanation:

Step1: Recall properties of each shape

• Parallelogram: Exactly 2 pairs of parallel sides, diagonals bisect each other, 4 congruent sides (if rhombus, a type of parallelogram), 4 right angles (if rectangle, a type of parallelogram).
• Trapezoid: Only 1 pair of parallel sides.
• Rhombus: Diagonals are perpendicular, 4 congruent sides, exactly 2 pairs of parallel sides (since it's a parallelogram), diagonals bisect each other.
• Rectangle: Diagonals are congruent, 4 right angles, exactly 2 pairs of parallel sides (since it's a parallelogram), diagonals bisect each other.

Step2: Match each property to the most specific shape

1. diagonals are congruent: This is a property of a rectangle (a type of parallelogram, but more specific than parallelogram as not all parallelograms have congruent diagonals).
2. diagonals bisect each other: This is a property of a parallelogram (all parallelograms have this, and it's a more general property, but if we consider the most specific, parallelogram is the base, but let's check others. Wait, rhombus and rectangle also have this, but the option says "other" maybe? Wait, no, let's re - check. Wait, the option "diagonals bisect each other" is a property of parallelogram (since trapezoid doesn't have this, rhombus and rectangle are parallelograms so they have it too, but the most specific shape for this general property is parallelogram).
3. only 1 pair of parallel sides: This is the definition of a trapezoid.
4. diagonals are perpendicular: This is a property of a rhombus (a type of parallelogram, more specific than parallelogram as not all parallelograms have perpendicular diagonals).
5. 4 congruent sides: This is a property of a rhombus (a type of parallelogram, more specific than parallelogram as not all parallelograms have 4 congruent sides).
6. exactly 2 pairs of parallel sides: This is a property of a parallelogram (trapezoid has 1, rhombus and rectangle are parallelograms so they have 2, but the most specific for this general property is parallelogram).
7. 4 right angles: This is a property of a rectangle (a type of parallelogram, more specific than parallelogram as not all parallelograms have 4 right angles).

Answer:

1. diagonals are congruent: Rectangle
2. diagonals bisect each other: Parallelogram
3. only 1 pair of parallel sides: Trapezoid
4. diagonals are perpendicular: Rhombus
5. 4 congruent sides: Rhombus
6. exactly 2 pairs of parallel sides: Parallelogram
7. 4 right angles: Rectangle