Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]

Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]

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APlusTopper.com provides step by step solutions for Selina Concise Mathematics Class 9 ICSE Solutions Chapter 14 Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]. You can download the Selina Concise Mathematics ICSE Solutions for Class 9 with Free PDF download option. Selina Publishers Concise Mathematics for Class 9 ICSE Solutions all questions are solved and explained by expert mathematic teachers as per ICSE board guidelines.

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Selina ICSE Solutions for Class 9 Maths Chapter 14 Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]

Exercise 14(A)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 1

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 2

Solution 3:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 3

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 4
In this linear equation n and k must be integer. Therefore to satisfy this equation the minimum value of k must be 6 to get n as integer.
Hence the number of sides are: 5 + 6 = 11.

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 5

Solution 6:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 6

Solution 7:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 7

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 8

Solution 9:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 9

Solution 10:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 10

Solution 11:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 11

Exercise 14(B)

Solution 1:
(i)True.
This is true, because we know that a rectangle is a parallelogram. So, all the properties of a parallelogram are true for a rectangle. Since the diagonals of a parallelogram bisect each other, the same holds true for a rectangle.
(ii)False
This is not true for any random quadrilateral. Observe the quadrilateral shown below.
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 12
Clearly the diagonals of the given quadrilateral do not bisect each other. However, if the quadrilateral was a special quadrilateral like a parallelogram, this would hold true.
(iii)False
Consider a rectangle as shown below.
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 13
It is a parallelogram. However, the diagonals of a rectangle do not intersect at right angles, even though they bisect each other.
(iv)True
Since a rhombus is a parallelogram, and we know that the diagonals of a parallelogram bisect each other, hence the diagonals of a rhombus too, bisect other.
(v)False
This need not be true, since if the angles of the quadrilateral are not right angles, the quadrilateral would be a rhombus rather than a square.
(vi)True
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 14
A parallelogram is a quadrilateral with opposite sides parallel and equal.
Since opposite sides of a rhombus are parallel, and all the sides of the rhombus are equal, a rhombus is a parallelogram.
(vii)False
This is false, since a parallelogram in general does not have all its sides equal. Only opposite sides of a parallelogram are equal. However, a rhombus has all its sides equal. So, every parallelogram cannot be a rhombus, except those parallelograms that have all equal sides.
(viii)False
This is a property of a rhombus. The diagonals of a rhombus need not be equal.
(ix)True
A parallelogram is a quadrilateral with opposite sides parallel and equal.
A rhombus is a quadrilateral with opposite sides parallel, and all sides equal.
If in a parallelogram the adjacent sides are equal, it means all the sides of the parallelogram are equal, thus forming a rhombus.
(x)False
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 15
Observe the above figure. The diagonals of the quadrilateral shown above bisect each other at right angles, however the quadrilateral need not be a square, since the angles of the quadrilateral are clearly not right angles.

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 16

Solution 3:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 17
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 18

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 19
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 20

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 21
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 22

Solution 6:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 23
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 24

Solution 7:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 25

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 26

Solution 9:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 27

Solution 10:
We know that AQCP is a quadrilateral. So sum of all angles must be 360.
∴ x + y + 90 + 90 = 360
x + y = 180
Given x:y = 2:1
So substitute x = 2y
3y = 180
y = 60
x = 120
We know that angle C = angle A = x = 120
Angle D = Angle B = 180 – x = 180 – 120 = 60
Hence, angles of parallelogram are 120, 60, 120 and 60.

Exercise 14(C)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 28

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 29

Solution 3:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 30

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 31

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 32

Solution 6:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 49
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 33

Solution 7:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 34
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 35

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 36

Solution 9:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 37
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 38

Solution 10:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 39

Solution 11:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 40

Solution 12:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 41

Solution 13:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 42

Solution 14:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 43

Solution 15:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 44

Solution 16:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 45

Solution 17:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 46

Solution 18:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 47

Solution 19:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 48

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