Give reason for the following:

(a) A square can be thought of as a special rectangle.

(b) A rectangle can be thought of as a special parallelogram.

(c) A square can be thought of as a special rhombus.

(d) Squares, rectangles, parallelograms are all quadrilaterals.

(e) Square is also a parallelogram.

(a) Yes a square is special rectangle, as a rectangle has its all angle of 90° and opposite sides are equals to each other. In the case of square all the angles are also of 90° and it has all the sides’ equals to each other.

(b) A rectangle has its all angles of 90° and opposite sides is equals and parallel to each other. A parallelogram also has opposite sides equal and parallel to each other. So we can say that a parallelogram with each angle a right angle becomes a rectangle and this rectangle can be thought of as a special parallelogram.

(c) All side of a rhombus are equal and a square also has all sides’ equals to each other with all the interior angles of 90°. A rhombus with each angle a right angle becomes a square. So, a square can be seen as a special rhombus.

(d) Squares, rectangles, parallelograms are all quadrilaterals as all of them have 4 line segments and all are closed figures.

(e) In a parallelogram opposite sides are equal and parallel and in a square opposite sides are equal and all the sides have same length so yes a square can be seen as a special parallelogram.