Let's analyze this geometry problem. We have a kite ABCD where side AB equals side AD, and side CB equals side CD. Our goal is to prove that diagonal AC is perpendicular to diagonal BD. Let's examine the given figure and understand the structure of this kite.The key insight is symmetry. Since AB equals AD, point A is equidistant from B and D. Similarly, since CB equals CD, point C is also equidistant from B and D. This means both A and C lie on the perpendicular bisector of segment BD. Therefore, the line AC must be perpendicular to BD at their intersection point O.