Trapezium

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

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

Solution 7:
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Solution 8:
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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.
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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.
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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:
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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:
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Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 29

Solution 3:
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Solution 4:
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Solution 5:
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Solution 6:
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Solution 7:
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Selina Concise Mathematics Class 9 ICSE Solutions Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] image - 35

Solution 8:
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Solution 9:
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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:
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Solution 12:
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Solution 13:
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Solution 14:
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Solution 15:
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Solution 16:
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Solution 17:
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Solution 18:
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Solution 19:
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What are the Different Kinds of Quadrilateral

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Different Types of Quadrilaterals

Quadrilaterals are categorised as the following, depending upon their sides.

  • Parallelogram
  • Rhombus
  • Rectangle
  • Square
  • Trapezium
  • Isosceles Trapezium
  • Kite

Parallelogram: A quadrilateral in which the pairs of opposite sides are parallel, is called a parallelogram.
Parallelogram In a parallelogram,

  1. Opposite sides are equal and parallel, i.e., AB = DC, BC = AD, AB || DC, and BC || AD.
  2. Opposite angles are equal, i.e., ∠A = ∠C and ∠B = ∠D.
  3. Diagonals bisect each other, i.e., AO = OC and BO = OD.
  4. Diagonal divides the parallelogram into two congruent triangles, i.e., ΔADC and ΔABC are congruent and ΔADB and ΔCBD are congruent.

Rectangle: A parallelogram in which each angle is a right angle, is called a rectangle.
RectangleIn a rectangle,

  1. Opposite sides are equal and parallel, i. e., AB = CD, AB || CD, BC = DA, and BC || DA.
  2. All angles are right angles, i.e., ∠A = ∠B = ∠C = ∠D = 90°.
  3. Both the diagonals are equal, i.e., AC = BD.
  4. Diagonals bisect each other, i.e., AR = RC and BR = RD.

Rhombus: A parallelogram in which all four sides are equal, is called a rhombus.
RhombusIn a rhombus,

  1. All sides are equal, i.e., PQ = QR = RS = SR
  2. Opposite sides are parallel, i.e., PQ || SR and SP || RQ.
  3. Opposite angles are equal, i.e., ∠P = ∠R and ∠Q = ∠S
  4. Diagonals bisect each other at right angle, i.e., PO = OR, SO = OQ and ∠SOR = ∠SOP = ∠ROQ = ∠QOP = 90°.

Square: A rhombus with all its angles equal to right angle, is called a square.
In other words, a square is a rectangle in which all the four sides are equal.
SquareIn a square,

  1. Opposite sides are parallel, i.e., AB || DC and AD || BC.
  2. All the sides are equal, i.e.,  AB = BC = CD = DA.
  3. All the angles are equal to 90°, i.e., ∠A = ∠B = ∠C = ∠D = 90°
  4. The diagonals bisect each other at right angle,
    i. e., AO = OC and BO = OD and ∠AOB = ∠BOC = ∠COD = ∠DOA = 90°
  5. Both the diagonals are equal in length, i.e., AC = BD.

Trapezium: A quadrilateral in which one pair of opposite sides are parallel, is called a trapezium.
TrapeziumIn a trapezium,

  1. A pair of opposite sides is parallel.
  2. Both the diagonals AC and BD are of different lengths.
  3. Diagonals do not bisect each other at right angle.
  4. Opposite angles are not equal.

Isosceles trapezium: A quadrilateral in which a pair of opposite sides is parallel and the other two sides are equal, is called an isosceles trapezium.
In an isosceles trapezium,

  1. A pair of opposite sides is parallel, i.e., AB || CD.
  2. Non-parallel sides are equal, i.e., AD = BC.
  3. Both the diagonals are equal, i.e., AC = BD.
  4. ∠A = ∠B and ∠D = ∠C.

Kite: A quadrilateral in which two pairs of adjacent sides are equal is called a kite.
KiteIn a kite,

  1. Two pairs of adjacent sides are equal, i.e., AB = AD and BC = CD.
  2. Diagonals intersect each other at right angle, i.e., ∠AEB = ∠AED = ∠BEC = ∠DEC = 90°.