Fill in the blanks with Always; Sometimes or Never: A trapezoid is sometimes a square. A chombus is never a parallelogram. A square is always a rhombus. A kite is sometimes a rhombus. A rhombus is sometimes a kite. Rectangles are never squares. Squares are sometimes rectangles. A rectangle is never a rhombus.
The Correct Answer and Explanation is:
Here are the correct answers for each statement:
- A trapezoid is sometimes a square.
Answer: Never
Explanation: A trapezoid, by definition, is a quadrilateral with at least one pair of parallel sides. A square, however, is a specific type of rectangle with all sides equal and all angles 90 degrees. Therefore, a trapezoid can never be a square because it does not have the required properties of equal sides and right angles. - A rhombus is never a parallelogram.
Answer: Never
Explanation: A rhombus is always a parallelogram because it satisfies all the properties of a parallelogram: opposite sides are parallel, opposite angles are equal, and the diagonals bisect each other at right angles. Therefore, a rhombus always fits the definition of a parallelogram. - A square is always a rhombus.
Answer: Always
Explanation: A square is a special type of rhombus. A rhombus is defined as a quadrilateral with all sides of equal length, and a square also has this property. Additionally, a square has the extra constraint of having right angles, but it still fulfills the basic properties of a rhombus, making it always a rhombus. - A kite is sometimes a rhombus.
Answer: Sometimes
Explanation: A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length. While some kites are also rhombuses (when all four sides are equal), not all kites have equal sides. Therefore, a kite is sometimes a rhombus. - A rhombus is sometimes a kite.
Answer: Always
Explanation: A rhombus is always a kite. In fact, a rhombus satisfies the properties of a kite because it has two pairs of adjacent sides that are equal. Therefore, a rhombus is always a kite. - Rectangles are never squares.
Answer: Never
Explanation: A rectangle is defined as a quadrilateral with four right angles, but it does not require that all sides be equal. A square is a special type of rectangle where all sides are equal. Therefore, rectangles can sometimes be squares, so the statement is incorrect. - Squares are sometimes rectangles.
Answer: Always
Explanation: A square is always a rectangle because a square has all the properties of a rectangle (four right angles), and it also has the added property that all sides are of equal length. Therefore, squares are always rectangles. - A rectangle is never a rhombus.
Answer: Never
Explanation: A rectangle has four right angles, but its sides do not necessarily have to be equal. A rhombus has all sides equal, which is a key difference. Therefore, a rectangle can never be a rhombus because it does not meet the requirement of equal side lengths.
