Question

retrieval
give the name of a geometric figure that fits the following characteristics:

1. a quadrilateral with four congruent sides 2. a quadrilateral with four congruent angles
2. a quadrilateral with opposite sides parallel

unit 1, lesson 3
8 of 10

Explanation:

Step1: Analyze characteristic 1

A quadrilateral with four congruent sides can be a rhombus or a square (since square is a special rhombus).

Step2: Analyze characteristic 2

A quadrilateral with four congruent angles (each \(90^\circ\)) is a rectangle or a square (square is a special rectangle).

Step3: Analyze characteristic 3

A quadrilateral with opposite sides parallel is a parallelogram, which includes rhombus, rectangle, square.

Step4: Find common figure

The figure that satisfies all three: four congruent sides (so rhombus - like), four congruent angles (right angles), and opposite sides parallel. This is a square (or also a rectangle - square is a rectangle with equal sides, but square fits all three as it has four equal sides, four right angles, and opposite sides parallel). Also, a square is a type of parallelogram, rhombus, and rectangle. But the most precise is square (or also rectangle? Wait, no: rectangle has four right angles but not necessarily four congruent sides unless it's a square. So square is the one that has four congruent sides (so satisfies 1), four congruent angles (90 each, satisfies 2), and opposite sides parallel (satisfies 3). Also, a rhombus doesn't have four congruent angles unless it's a square. A rectangle doesn't have four congruent sides unless it's a square. So square is the figure that fits all three. Alternatively, a square is a type of parallelogram, but parallelogram doesn't necessarily have four congruent sides or four congruent angles. So the key is the intersection of the three: four congruent sides (so rhombus family), four congruent angles (rectangle family), so their intersection is square. Also, a square has opposite sides parallel (as it's a parallelogram). So the figure is a square (or also a rectangle? No, rectangle has two pairs of congruent sides, not four unless square. So square is the one with four congruent sides, four congruent angles, and opposite sides parallel. Also, a square is a quadrilateral, so that's the figure.

Answer:

Square (also, a square is a special case of rhombus, rectangle, and parallelogram; another possible answer could be rectangle but rectangle doesn't have four congruent sides unless it's a square, so square is more precise. Alternatively, if we consider that a square is a type of rectangle, but the first characteristic requires four congruent sides, so square is the best fit.)