Which statement is true?
1) A quadrilateral is always a parallelogram. 2) A square is always a parallelogram. 3) A trapezoid never has two congruent sides. 4) A parallelogram is never a rhombus.
The Correct Answer and Explanation is:
The correct statement is 2) A square is always a parallelogram.
Explanation:
Let’s go over each statement one by one:
- A quadrilateral is always a parallelogram.
- This is false. A quadrilateral is a polygon with four sides, but not all quadrilaterals are parallelograms. A parallelogram is a specific type of quadrilateral where opposite sides are parallel and equal in length. However, there are other types of quadrilaterals, such as trapezoids and kites, that are not parallelograms.
- A square is always a parallelogram.
- This statement is true. A square is a specific type of parallelogram. A parallelogram has opposite sides that are parallel and equal in length. A square satisfies these conditions, but it also has the additional properties of having all four sides equal in length and all four angles equal to 90 degrees. Thus, by definition, a square is a parallelogram, but with more specific properties.
- A trapezoid never has two congruent sides.
- This statement is false. A trapezoid is a quadrilateral with at least one pair of parallel sides. It can have two congruent (equal-length) non-parallel sides. When this happens, the trapezoid is specifically called an isosceles trapezoid. Therefore, it is possible for a trapezoid to have two congruent sides.
- A parallelogram is never a rhombus.
- This statement is false. A rhombus is a specific type of parallelogram where all four sides have equal length. Since all rhombuses are parallelograms (they meet the criteria of having opposite sides parallel), this statement is incorrect.
Therefore, the correct answer is 2) A square is always a parallelogram, as a square is a special type of parallelogram with additional properties.