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.
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.
(a) In a rectangle, all the interior angles are of the same measure,
i.e., 90º and only the opposite sides of the rectangle are of
the same length whereas 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. Therefore,
a square is a special rectangle.
(b) 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., 90º.
In other words, a parallelogram with each angle a right angle becomes
a rectangle. Therefore, a rectangle can be thought of as a special
parallelogram.
(c) All sides of a rhombus and a square are equal. However, in case
of a square, all interior angles are of 90º measure. A rhombus
with each angle a right angle becomes a square. Therefore, a square
can be thought of as a special rhombus.
(d) All are closed figures made of 4 line segments. Therefore, all
these are quadrilaterals.
(e) Opposite sides of a parallelogram are parallel and equal. In a
square, the opposite sides are parallel and the lengths of all the
four sides are equal. Therefore, a square can be thought of as a
special parallelogram.
(a) In a rectangle, all the interior angles are of the same measure, i.e., 90º and only the opposite sides of the rectangle are of the same length whereas 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. Therefore, a square is a special rectangle.
(b) 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., 90º. In other words, a parallelogram with each angle a right angle becomes a rectangle. Therefore, a rectangle can be thought of as a special parallelogram.
(c) All sides of a rhombus and a square are equal. However, in case of a square, all interior angles are of 90º measure. A rhombus with each angle a right angle becomes a square. Therefore, a square can be thought of as a special rhombus.
(d) All are closed figures made of 4 line segments. Therefore, all these are quadrilaterals.
(e) Opposite sides of a parallelogram are parallel and equal. In a square, the opposite sides are parallel and the lengths of all the four sides are equal. Therefore, a square can be thought of as a special parallelogram.
