Selina solutions concise maths class 9 icse Solutions for Chapter 11 chapter 11 inequalities

Exercises in Chapter 11 chapter 11 inequalities Grade 9

Exercise11

Questions in Exercise11

From the following figure, prove that:

AB>CD

$\text { In a triangle } P Q R ; Q R=P R \text { and } \angle P=360 \text { . Which is the largest side of the triangle? }$

If two sides of a triangle are 8 cm and 13 cm, then the length of the third side is between a

cm and b cm. Find the values of a and b such that a is less than b.

In each of the following figures write BC, AC, and CD in ascending order of their lengths.

(i)

Arrange the sides of triangle BOC in descending order of their lengths. BO and CO are

bisectors of angles ABC and ACB respectively.

D is a point in side BC of triangle ABC. If AD>AC, show that AB>AC.

In the following figure, BAC = 600 and ABC = 650.

Prove that:

(i) CF > AF

(ii) DC > DF

From the following figure; prove that:

(i) AB > BD

(ii) AC > CD

(iii) AB + AC > BC

In a quadrilateral ABCD; prove that:

(i) AB + BC + CD > DA

(ii) AB + BC + CD + DA > 2AC

(iii) AB + BC + CD + DA > 2BD

In the following figure, ABC is an equilateral triangle and P is any point in AC; prove that:

(i) BP > PA

(ii) BP > PC

$\mathrm{P} \text { is any point inside the triangle } \mathrm{ABC} . \text { Prove that: } \angle \mathrm{BPC}>\angle \mathrm{BAC} \text { . }$

$\text { In triangle } \mathrm{ABC} ; \mathrm{AB}=\mathrm{AC} \text { and } \angle \mathrm{A}: \angle \mathrm{B}=85 ; \text { find } \angle \mathrm{A} \text { . }$

Prove that the straight line joining the vertex of an isosceles triangle to any point in the

the base is smaller than either of the equal sides of the triangle.

In the following diagram; AD = AB and AE bisects angle A. Prove that:

(i) BE = DE

$(\text { ii) } \quad \angle \mathrm{ABD}>\angle \mathrm{C}$

The sides AB and AC of a triangle ABC are produced; and the bisectors of the external

angles at B and C meet at P. Prove that if AB>AC, then PC > PB.

In the following figure; AB is the largest side and BC is the smallest side of triangle ABC.

In quadrilateral ABCD, side AB is the longest, and side DC is the shortest. Prove that:

$\text { (i) } \angle \mathrm{C}>\angle \mathrm{A}$

$\text { (ii) } \angle \mathbf{D}>\angle \mathbf{B}$

In triangle ABC, side AC is greater than side AB. If the internal bisector of angle A meets

the opposite side at point D, prove that: $\angle \mathrm{ADC} \text { is greater than } \angle \mathrm{ADB}$

An isosceles triangle ABC, sides AB and AC are equal. If point D lies in base BC and point

E lies on BC produced (BC being produced through vertex C), prove that:

(i) AC > AD

(ii) AE > AC

(iii) AE > AD

Given: ED = EC

Prove: AB + AD > BC

In triangle ABC, AB > AC and D is a point in side BC. Show that: AB>AD.

Was This helpful?

Chapters in this book

Chapter 1- Rational and Irrational Numbers

Chapter 2- Compound Interest [Without Using Formula

Chapter 3- Compound Interest [Using Formula

Chapter 4- Expansions

Chapter 5- Factorisation

Chapter 6- Simultaneous Equations

Chapter 7- Indices [exponents]

Chapter 8- Logarithms

Chapter 9- Triangles [Congruency in Triangles]

Chapter 10- Isosceles Triangle

Chapter 11- Inequalities

Chapter 12- Mid-Point and Its Converse

Chapter 13- Pythagoras Theorem

Chapter 14- Rectilinear Figures

Chapter 15- Construction of Polygons

Chapter 16- Area Theorems

Chapter 17- Circles

Chapter 18- Statistics

Chapter 19- Mean and Median

Chapter 20- Area and Perimeter of Plane Figures

Chapter 21- 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

Chapter 28- Distance Formula