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Yes. A figure which is both a rhombus and a rectangle is commonly called a square.
Yes. A square is both a rhombus and a rectangle. A rectangles is a figure with four right angles, and all squares do indeed have four right angles. A rhombus has four equal sides, and all squares meet this requirement.
A rectangle can sometimes be a rhombus, as a square is both a rectangle and a rhombus. However, if all sides are congruent, and it has right angles, it is a square and therefore not a rectangle. So, the answer is no, although it may be argued to be yes. Wikipedia, in fact, mentions that a square is both a rectangle and a rhombus; the definition of rectangle there is a quadrilateral with four right angles, thereby not excluding the special case of a rectangular rhombus, or a square. A rhombus is not normally a square but it could be.
nothing fits the definition of rhombus and rectangles becauses the definition for rectangle is : a plane figure with four straight sides and FOUR RIGHT ANGLESbut the definition of rhombus is...a parallelogram with ,OPPOSITE EQUAL ACUTE ANGLES and OPPOSITE EQUAL OBTUSE ANGLES, and four equal sides.
Sometimes a Rectangle can be a Rhombus.