Which Of the Following statements is always true? A) Every Rhombus is also a square B) Every Rectangle is also a trapezoid C) every rectangle is also a parallelogram D) every parallelogram is also a rhombus Which Of the Following statements is always true? A) Every Rhombus is also a square B) Every Rectangle is also a trapezoid C) every rectangle is also a parallelogram D) every parallelogram is also a rhombus
The Correct Answer and Explanation is :
The statement that is always true is: C) Every rectangle is also a parallelogram.
To understand why this is the case, let’s analyze each statement in detail:
A) Every rhombus is also a square.
A rhombus is defined as a quadrilateral with all four sides of equal length. However, the angles in a rhombus are not necessarily right angles. A square, on the other hand, is a special type of rhombus where all four sides are equal, and all four angles are right angles (90 degrees). Since a rhombus does not require right angles, not every rhombus is a square.
B) Every rectangle is also a trapezoid.
A rectangle is a quadrilateral with opposite sides equal and all angles equal to 90 degrees. A trapezoid (in American English) is defined as a quadrilateral with at least one pair of parallel sides. Under the inclusive definition, parallelograms (including rectangles) are considered trapezoids because they have two pairs of parallel sides. However, under the exclusive definition, a trapezoid has exactly one pair of parallel sides, excluding parallelograms. Therefore, whether every rectangle is also a trapezoid depends on the definition adopted, making this statement not universally true.
C) Every rectangle is also a parallelogram.
A parallelogram is defined as a quadrilateral with two pairs of parallel sides. A rectangle fits this definition because it has two pairs of parallel sides, with opposite sides being equal in length and all angles equal to 90 degrees. Therefore, every rectangle is a specific type of parallelogram.
D) Every parallelogram is also a rhombus.
While a parallelogram has two pairs of parallel sides with opposite sides equal in length, a rhombus requires all four sides to be of equal length. Not all parallelograms meet this criterion; for example, a rectangle is a parallelogram but not a rhombus unless all its sides are equal. Therefore, not every parallelogram is a rhombus.
In summary, the only statement that is always true is C) Every rectangle is also a parallelogram, as a rectangle inherently satisfies all the properties of a parallelogram.