Chapter - 5- EXERCISE 5.7 - Basic Geometrical Ideas (NCERT Class 6th Maths Solution)

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/Explanation:

(i) In a rectangle, each angle is a right angle. TRUE

(ii) In a rectangle, the opposite sides are equal in length. TRUE

(iii) In a square, the diagonals are perpendicular to each another. TRUE

(iv) In a rhombus, all the sides are equal in length. TRUE

(v) In a parallelogram, all the sides are equal in length. FALSE

(vi) In a trapezium, the opposite sides are parallel. 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/Explanation:

a)because square have all properties of rectangle but rectangle does not have all properties of square.
b)because parallelogram have all properties of rectangle but rectangle does not have all properties of parallelogram.
c)because square have all properties of rhombus but rhombus does not have all properties of square.
d) properties of quadrilateral are that they have 4 sides and sum of 4 angles is 360 0       which are same as quare,rectangle,parallelogram.
e)because square have parallel sides and sum of all 4 angles is 3600

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/Explanation:

Square is a regular quadrilateral as all sides and angles are equal.

As per the property mentioned above,

$1).$ All sides are equal

$2).$ All angles are $90^{\circ }$ (means equal). 

Now, the property of the regular quadrilateral,

$1).$ All sides are equal

$2).$ All angles are equal

Hence, the given figure can be identified as the regular quadrilateral.