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Understanding Elementary Shapes
1. Say True or False :
(a) Each angle of a rectangle is a right angle.
(b) The opposite sides of a rectangle are equal in length.
(c) The diagonals of a square are perpendicular to one another.
(d) All the sides of a rhombus are of equal length.
(e) All the sides of a parallelogram are of equal length.
(f) The opposite sides of a trapezium are parallel.
Solution: (a) True.
2. 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.
Solution: (a) In a rectangle opposite sides are equal and parallel to each other, also all interior angles are equal to 900. If all sides of the rectangle are equal it will form a square. So, a square is a special rectangle with equal sides.
(b) In parallelogram opposite sides are equal and parallel to each other same as in the rectangle. In a rectangle, all interior angles are equal to 900. So, a parallelogram with each angle as a right-angle form a rectangle. Hence, a rectangle can be thought of as a special parallelogram.
(c) All sides are equal in both square and rhombus. In the square, all interior angles are equal to 900. So, a rhombus with each angle as a right-angle form a square. Hence, a square can be thought of as a special rhombus.
(d) All figures having four sides are called a quadrilateral. Therefore, Squares, rectangles, parallelograms are all quadrilaterals.
(e) In parallelogram opposite sides are equal and opposite whereas in the square opposite sides are parallel and all 4 sides are equal. Therefore, a square is also a parallelogram.
3. A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?
Solution: Square. All 4 sides of a square are equal and all interior angles are equal to 900. So, it is a regular quadrilateral.
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