What is the method to prove that a figure is a square?

To demonstrate that a figure is a square, one must confirm that all sides are equal in length and that the diagonals are also equal. This is essential because a square is a specific type of rectangle that not only has equal opposite sides and right angles but also has all four sides equal in length.

When all sides are equal, the figure is at least a rhombus. However, for it to also be classified as a square, the diagonals must be equal in addition to the sides being equal. Equal diagonals are a characteristic of rectangles, and since a square is a rectangle as well, fulfilling both criteria confirms that the figure is indeed a square.

In contrast, simply demonstrating one pair of parallel sides does not provide sufficient evidence of the properties required for a square. Showing only two pairs of opposite sides being equal describes a parallelogram, which could include various types of quadrilaterals, not specifically a square. Lastly, while proving that all angles are right angles indicates a rectangle, without the equal sides condition, the figure cannot be confirmed as a square. Therefore, the method that accurately establishes a figure as a square requires the verification of both equal sides and equal diagonals.