Givereasons for the following:
(a) Asquare can be thought of as a special rectangle.
(b) Arectangle can be thought of as a special parallelogram.
(c) Asquare can be thought of as a special rhombus.
(d) Squares,rectangles, parallelograms are all quadrilaterals.
(e) Squareis also a parallelogram.
Givereasons for the following:
(a) Asquare can be thought of as a special rectangle.
(b) Arectangle can be thought of as a special parallelogram.
(c) Asquare can be thought of as a special rhombus.
(d) Squares,rectangles, parallelograms are all quadrilaterals.
(e) Squareis 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 ofthe same length whereas in case of a square, all the interior anglesare of 90° and all the sides are of the same length. In otherwords, 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 arectangle, the opposite sides are parallel and equal. Also, all theinterior angles of the rectangle are of the same measure, i.e., 90º.In other words, a parallelogram with each angle a right angle becomesa rectangle. Therefore, a rectangle can be thought of as a specialparallelogram.
(c) All sides of a rhombus and a square are equal. However, in caseof a square, all interior angles are of 90º measure. A rhombuswith each angle a right angle becomes a square. Therefore, a squarecan be thought of as a special rhombus.
(d) All are closed figures made of 4 line segments. Therefore, allthese are quadrilaterals.
(e) Opposite sides of a parallelogram are parallel and equal. In asquare, the opposite sides are parallel and the lengths of all thefour sides are equal. Therefore, a square can be thought of as aspecial 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 ofthe same length whereas in case of a square, all the interior anglesare of 90° and all the sides are of the same length. In otherwords, 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 arectangle, the opposite sides are parallel and equal. Also, all theinterior angles of the rectangle are of the same measure, i.e., 90º.In other words, a parallelogram with each angle a right angle becomesa rectangle. Therefore, a rectangle can be thought of as a specialparallelogram.
(c) All sides of a rhombus and a square are equal. However, in caseof a square, all interior angles are of 90º measure. A rhombuswith each angle a right angle becomes a square. Therefore, a squarecan be thought of as a special rhombus.
(d) All are closed figures made of 4 line segments. Therefore, allthese are quadrilaterals.
(e) Opposite sides of a parallelogram are parallel and equal. In asquare, the opposite sides are parallel and the lengths of all thefour sides are equal. Therefore, a square can be thought of as aspecial parallelogram.
