Exercise 5.7 - Chapter 5 - Understanding elementary shapes - Ncert Solutions class 6 - Maths

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Question 1:

Say True of 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.

Answer:

(a) True

(b) True

(c) True

(d) True

(e) False

(f) False

Question 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.

Answer:

(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.

Question 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?

Answer:

In a square, all the interior angles are of 90° and all the sides are of the same length. Therefore, a square is a regular quadrilateral.