Short Answer 
The diagonals of a square are congruent, meaning they are equal in length, and they intersect perpendicularly at right angles. Additionally, the diagonals bisect the vertex angles, with each angle being divided evenly at 45 degrees.
Step 1: Understand Diagonal Congruence
In a square, the diagonals, namely AC and DB, are congruent to each other. This means they are equal in length, which is a unique property of squares. This congruence ensures that the square is symmetrical along both diagonals.
Step 2: Explore Diagonal Perpendicularity
The diagonals of a square intersect at right angles, making them perpendicular. This means that the angles formed at their intersection (m‚a†AOB, m‚a†AOD, m‚a†COD, and m‚a†BOC) each measure 90 degrees. This characteristic contributes to the overall symmetry and balance of the square.
Step 3: Analyze Angle Bisection
The diagonals of a square also bisect the vertex angles. For example, at vertex A, angles DAC and BAC are each 45 degrees. This property holds true for all four vertices of the square, ensuring that each angle is evenly divided by the intersecting diagonals.