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

Class 9: Maths Chapter 14 solutions. Complete Class 9 Maths Chapter 14 Notes.

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

Selina 9th Maths Chapter 14, Class 9 Maths Chapter 14 solutions

Exercise 14(A)

Solution 1:

Solution 2:

Solution 3:

Solution 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 10:

Solution 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.

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.

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

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

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.

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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)

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Solution 19:

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

Download PDF: Selina Class 9 ICSE Solutions Mathematics : Chapter 14- Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium] PDF

Chapterwise Selina Publishers ICSE Solutions for Class 9 Mathematics :

• Chapter 1 - Rational and Irrational Numbers
• Chapter 2- Compound Interest (Without using formula)
• Chapter 3 - Compound Interest (Using Formula)
• Chapter 4- Expansions (Including Substitution)
• Chapter 5- Factorisation
• Chapter 6 - Simultaneous (Linear) Equations (Including Problems)
• Chapter 7- Indices (Exponents)
• Chapter 8- Logarithms
• Chapter 9- Triangles [Congruency in Triangles]
• Chapter 10- Isosceles Triangles
• Chapter 11- Inequalities
• Chapter 12- Mid-point and Its Converse [ Including Intercept Theorem]
• Chapter 13- Pythagoras Theorem [Proof and Simple Applications with Converse]
• Chapter 14- Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
• Chapter 15- Construction of Polygons
• Chapter 16- Area Theorems [Proof and Use]
• Chapter 17- Circle
• Chapter 18- Statistics
• Chapter 19- Mean and Median
• Chapter 20 - Area and Perimeter of Plane Figures
• Chapter 21- Solids [Surface Area and Volume of 3-D Solids]
• Chapter 22- Trigonometrical Ratios
• Chapter 23- Trigonometrical Ratios of Standard Angles
• Chapter 24- Solution of Right Triangles
• Chapter 25- Complementary Angles
• Chapter 26- Co-ordinate Geometry
• Chapter 27- Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)
• Chapter 28- Distance Formula

About Selina Publishers ICSE

Selina Publishers has been serving the students since 1976 and is one of the quality ICSE school textbooks publication houses. Mathematics and Science books for classes 6-10 form the core of our business, apart from certain English and Hindi literature as well as a few primary books. All these books are based upon the syllabus published by the Council for the I.C.S.E. Examinations, New Delhi. The textbooks are composed by a panel of subject experts and vetted by teachers practising in ICSE schools all over the country. Continuous efforts are made in complying with the standards and ensuring lucidity and clarity in content, which makes them stand tall in the industry.