Square Properties 4Fab75

1. **Problem:** Determine which statements are always true for a square. 2. **Recall properties of a square:** - All sides are equal. - All angles are right angles ($90^\circ$). - Diagonals are equal in length. - Diagonals bisect each other at right angles. - Diagonals bisect the angles of the square. - Opposite angles in a square are equal (both $90^\circ$). 3. **Evaluate each statement:** - "The diagonals bisect the angles of the quadrilateral." \(\rightarrow\) True for a square because each diagonal splits the $90^\circ$ angles into two $45^\circ$ angles. - "The diagonals are equal." \(\rightarrow\) True, diagonals of a square have equal length. - "The opposite angles are equal." \(\rightarrow\) True, all angles in a square are $90^\circ$, so opposite angles are equal. - "The diagonals intersect each other at right angles." \(\rightarrow\) True, diagonals of a square intersect at $90^\circ$. - "None of these." \(\rightarrow\) False, since multiple statements are true. 4. **Final answer:** The first four statements are always true for a square. "None of these" is false.