Final answer:
To determine if a quadrilateral is a square from a diagram, look for equal side lengths and right angles, use the Pythagorean theorem if appropriate, and solve any provided equations for unknown values.
Step-by-step explanation:
Assuming a quadrilateral is a square from a diagram, without explicit markings indicating right angles or equal side lengths, can be incorrect. To verify if a quadrilateral indeed is a square, we should look for certain characteristics that define a square, which include four equal side lengths and four right angles. A helpful trick to reaffirm these properties might be to compare the quadrilateral with a square's known attributes, such as a perimeter equivalent to 4 times the side length (4a), and an area that equals the side length squared (a²).
From the diagram, you can also use the Pythagorean theorem in cases where a right triangle is involved, ensuring that the square of the hypotenuse is equal to the sum of the squares of the other two sides. If the quadrilateral can be fitted into a larger square with known dimensions, you can determine if the smaller figure has sides of equal length and each angle measuring 90 degrees, which are defining characteristics of a square.
Finally, if given numeric values, you may be required to solve an equation, perhaps using the quadratic formula or by simplifying the expression into a perfect square, to find unknown dimensions that could confirm the quadrilateral's nature as a square.