Chapter - 5 Understanding Elementary Shapes

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Q
Understanding Elementary Shapes

Question:

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.

(b) True.

(c) True.

(d) True.

(e) False.

(f) False.

 

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.

Answer:


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