1. Let's start by stating the problem: Can a shape be both a trapezoid and a kite? What are the conditions for each shape? 2. Definitions: - A trapezoid is a quadrilateral with at least one pair of parallel sides. - A kite is a quadrilateral with two pairs of adjacent sides equal in length. 3. To be both a trapezoid and a kite, the shape must satisfy both conditions simultaneously. 4. Consider a quadrilateral with one pair of parallel sides (making it a trapezoid). 5. Now, if the non-parallel sides are equal in pairs and adjacent, it also satisfies the kite condition. 6. For example, an isosceles trapezoid with the non-parallel sides equal in length is both a trapezoid and a kite. 7. This is possible because the definitions overlap: the trapezoid requires parallel sides, and the kite requires pairs of adjacent equal sides, which can coexist. 8. Therefore, a shape can be both a trapezoid and a kite if it has one pair of parallel sides and two pairs of adjacent equal sides. Final answer: Yes, a shape can be both a trapezoid and a kite if it has one pair of parallel sides and two pairs of adjacent equal sides.