NCERT Solutions for Class 6 Mathematics Chapter 5 Understanding Elementary Shapes Exercise 5.7

Exercise 5.7

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Ex-5.1
Ex-5.2
Ex-5.3
Ex-5.4
Ex-5.5
Ex-5.6
Ex-5.7
Ex-5.8
Ex-5.9

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Q 1 - Ex 5.7 - Understanding Elementary Shape - NCERT Maths Class 6th - Chapter 5

Page No 106:

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

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Q 2 - Ex 5.7 - Understanding Elementary Shape - NCERT Maths Class 6th - Chapter 5

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.

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Q 3 - Ex 5.7 - Understanding Elementary Shape - NCERT Maths Class 6th - Chapter 5

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.