What type of quadrilateral is ABCD if all four sides are congruent but the opposite angles are not equal?

To determine the type of quadrilateral, we need to analyze the given information.

In this case, we know that all four sides of quadrilateral ABCD are congruent, but the opposite angles are not equal. Let's go through the steps to understand the specific type of quadrilateral.

1. First, we know that a quadrilateral is a polygon with four sides. So, every quadrilateral has four angles and four sides.

2. Since all four sides of ABCD are congruent, we can conclude that it is a special type of quadrilateral known as a rhombus. A rhombus is defined as a quadrilateral with all sides of equal length.

3. However, the given information also mentions that the opposite angles are not equal. A rhombus has opposite angles that are congruent, so ABCD cannot be a rhombus.

4. When we consider a quadrilateral with four congruent sides and non-equal opposite angles, we find that it matches the characteristics of a kite.

5. Therefore, the type of quadrilateral ABCD is a kite. A kite is a quadrilateral with two pairs of adjacent sides that are congruent, but the opposite angles are not equal.

In summary, if all four sides of a quadrilateral are congruent, but the opposite angles are not equal, then it is a kite.