1. The problem is to explain the properties of a square as shown in the picture and provide examples of its angles, sides, and diagonals. 2. A square is a special type of parallelogram that is both a rectangle and a rhombus. This means it has all the properties of both shapes. 3. Key properties of a square include: - Four equal sides: all sides have the same length, for example, if one side is $s$, then all sides are $s$. - Four equal angles: each angle is $90^\circ$, meaning all corners are right angles. - Diagonals are equal in length: if the side length is $s$, each diagonal has length $d = s\sqrt{2}$. - Diagonals bisect each other: the diagonals cut each other exactly in half. - Diagonals are perpendicular: they intersect at right angles ($90^\circ$). 4. In the picture: - The four light blue sides represent the equal sides of the square. - The pink corners mark the four right angles ($90^\circ$) at each vertex. - The two black diagonals cross inside the square, showing they bisect each other. - The pink square symbol at the intersection of the diagonals indicates the diagonals are perpendicular. - The black hash marks on the diagonals show that each diagonal is divided into two equal parts. 5. Example: If each side of the square is $4$ units, then: - Each angle is $90^\circ$. - Each diagonal length is $$d = 4\sqrt{2} \approx 5.66$$ units. - The diagonals intersect at their midpoints, each segment being half the diagonal length, about $2.83$ units. This explanation covers the visual and geometric properties of the square shown in the picture.