The table shows the properties of three different quadrilaterals. Square Rectangle Parallelogram All sides congruent ? × × Opposite sides congruent ? ? ? All angles congruent ? ? × Opposite angles congruent ? ? ? Diagonals congruent ? ? × Diagonals bisect ? ? ? Correct! You have completed this exercise.
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The Correct Answer and Explanation is:
Corrected Table with Answers Filled In:
| Property | Square | Rectangle | Parallelogram |
|---|---|---|---|
| All sides congruent | ✓ | × | × |
| Opposite sides congruent | ✓ | ✓ | ✓ |
| All angles congruent | ✓ | ✓ | × |
| Opposite angles congruent | ✓ | ✓ | ✓ |
| Diagonals congruent | ✓ | ✓ | × |
| Diagonals bisect | ✓ | ✓ | ✓ |
Explanation
Quadrilaterals are polygons with four sides, and they have different properties based on their classification. A square, rectangle, and parallelogram are all types of quadrilaterals, but each has unique characteristics.
A square is the most regular of the three. It has all four sides congruent and all angles equal to 90 degrees. Opposite sides are not only congruent, but adjacent sides are also congruent. All angles are congruent, and the diagonals are equal in length and bisect each other at right angles. This means a square satisfies all six properties listed in the table.
A rectangle shares some traits with a square. All its angles are 90 degrees, making all angles congruent. Opposite sides are congruent and parallel. Diagonals in a rectangle are also congruent, but unlike a square, not all sides are equal. Therefore, it does not satisfy the “all sides congruent” condition.
A parallelogram has opposite sides that are congruent and parallel. Opposite angles are congruent, and the diagonals bisect each other. However, not all angles are necessarily equal — they can be acute or obtuse — and the diagonals are not necessarily congruent. Also, its sides are only congruent in pairs, not all four.
In summary, all three figures have opposite sides congruent and diagonals that bisect. Only the square meets all criteria. The rectangle lacks equal side lengths, and the parallelogram lacks equal angles and diagonals. This comparison helps students understand geometric classifications through properties and reinforces the hierarchy within quadrilaterals.
