In Euclidean geometry, consider the statement Every square is a rhombus. Is this statement correct or incorrect for all squares?

Introduction / Context:
Geometry questions in reasoning tests often check understanding of definitions and relationships between standard shapes. This question examines how squares and rhombuses are related. Specifically, it asks whether every square can be classified as a rhombus. To answer correctly, we must recall the formal definitions of both shapes and see whether one definition automatically satisfies the other.

Given Data / Assumptions:

• A square is a quadrilateral with four equal sides and four angles of 90 degrees.
• A rhombus is a quadrilateral with four equal sides, but its angles need not be right angles.
• We work in standard Euclidean geometry with usual plane figures.
• The statement under review is: Every square is a rhombus.

Concept / Approach:
To see whether every square is a rhombus, we check if a square satisfies the rhombus definition. The definition of a rhombus requires only that all sides are equal. The definition of a square goes further by adding the extra condition that all interior angles are right angles. Thus, a square satisfies all the conditions of a rhombus, and more. This means that a square is a special case of a rhombus that has extra angle properties, so the statement under consideration is correct.

Step-by-Step Solution:
Step 1: Recall rhombus definition: a quadrilateral with all four sides equal. Step 2: Recall square definition: a quadrilateral with all four sides equal and all four angles equal to 90 degrees. Step 3: Compare the two definitions. Every square has four equal sides, so it automatically satisfies the rhombus side condition. Step 4: The extra condition of right angles in a square does not violate the rhombus definition. It only makes the square a more specific case. Step 5: Therefore the statement Every square is a rhombus is correct for all squares.

Verification / Alternative check:
You can imagine the family tree of quadrilaterals. At the top is the general quadrilateral. A rhombus is a special type where all sides are equal. A square is an even more specialized rhombus that also has four right angles. So, the inclusion chain is: quadrilateral, then rhombus, then square. From this hierarchy it is clear that each square is automatically included in the set of rhombuses, which confirms that the statement is correct.

Why Other Options Are Wrong:
Incorrect, a square is never a rhombus: This is false because a square fulfils the rhombus side condition of four equal sides.
Correct only for some squares, not for all: There is no such restriction. Every square has equal sides, so the relationship is universal, not partial.
Cannot be decided from the given information: The definitions are standard and sufficient, so the truth of the statement can be decided clearly.
The statement is reversed because every rhombus is a square: This is wrong. A rhombus does not need to have right angles, so many rhombuses are not squares. The reverse statement is false.

Common Pitfalls:
A frequent mistake is to confuse the conditions and think that because a square has right angles, it must be different from a rhombus. Another confusion is reversing the subset relationship and assuming that if all sides are equal, then it must be a square, which is not correct. Always pay attention to which shape adds more conditions and which shape has looser conditions.

Final Answer:
The statement is Correct; every square is indeed a special type of rhombus with right angles.