Quadrilateral ABCD has all congruent sides and opposite angles that are congruent. What classification can be given to ABCD?
Congruent means coinciding exactly when superimposed. All sides are equal means, it can be a square or a rhombus. But now opposite angles (let angles be x and y) are also congruent. This implies
2x + 2y = 360 degrees (sum of all angles of a quadrilateral is 360 degrees)
x + y = 180 degrees.
This is a rhombus (a kite with all sides equal).