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Give reasons 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.

Answer:

(a) A rectangle in which all the interior angles are of same measure i.e 90° and only opposite sides of the rectangle are of same length whereas in square all the interior angles are of 90° and all the sides of the square are of same length. Hence, a rectangle with all sides equal becomes a square. Therefore square is a special rectangle.

(b) In a parallelogram opposite sides are parallel and equal. In a rectangle opposite sides are parallel and equal. The interior angles of the rectangle are of same measure i.e 90° . Hence, a parallelogram with each angle as right angle becomes a square. Therefore a rectangle is a special parallelogram

(c) All sides of a rhombus and square are equal but in case of square all interior angles are of 90° . A rhombus with each angle as right angle becomes a square. Therefore a square is a special rhombus

(d) Since, all are closed figures with 4 line segments. Hence all are quadrilaterals

(e) Opposite sides of a parallelogram are equal and parallel whereas in a square opposite sides are parallel and all 4 sides are of same length. Therefore a square is a special parallelogram.

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