+2 votes
by kratos

Give reasons for the following:

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

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

(c) A square can be through of as a special parallelogram.

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

(e) Square is also a parallelogram.

1 Answer

+6 votes
by kratos
 
Best answer

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

In a rectangle all the interior angles are of the same measure i,e, 90° and the opposite side of the rectangle are of the same length where as in case of a square, all the interior angles are of 90° and all the sides are of the same length in other words, a rectangle with all sides equal becomes a square there, a square is a special rectangle.

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

Opposite sides of a parallelogram are parallel and equal in a rectangle, the opposite sides are parallel and equal also, all the interior angles of the rectangle are of the same Measure, i,e. 90°. in other words, a parallelogram with each angle a right angle becomes a rectangle Therefore a rectangle can be thought of as a specific parallelogram.

(c) A square can be through of as a special parallelogram.

All sides of a rhombus and a square are equal However, in case of a square, all interior angles are of 90° Measure. A rhombus with each angle a right angle becomes a square Therefore a square can be thought of as a special rhombus.

(d) Squares, rectangles, parallelograms are all quadrilaterals.
All are closed figure made of 4 line segments Therefore all these are quadrilaterals.

(e) Square is also a parallelogram. Opposite sides of a parallelogram are parallel and equal in a square, the opposite sides are parallel and the lengths of the four sides are equal Therefore a square can be thought 6 f as a special parallelogram.

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