Chapter 13 : Inequalities in Triangles - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

Read  more
Page / Exercise

Chapter 13 - Inequalities in Triangles Excercise Ex. 13.1

Question 1

Name the greatest and the smallest sides in the following triangles:

ABC, ∠ = 56o, ∠B = 64o and ∠C = 60o.

Solution 1

 

Question 2

Name the greatest and the smallest sides in the following triangles:

DEF, ∠D = 32o, ∠E = 56o and ∠F = 92o.

Solution 2

Question 3

Name the greatest and the smallest sides in the following triangles:

XYZ, ∠X = 76o, ∠Y = 84o.

Solution 3

 

Question 4

Arrange the sides of the following triangles in an ascending order:

ABC, ∠A = 45o, ∠B = 65o.

Solution 4

Question 5

Arrange the sides of the following triangles in an ascending order:

DEF, ∠D = 38o, ∠E = 58o.

Solution 5

Question 6
Solution 6
Question 7

In a triangle ABC, BC = AC and ∠ A = 35°. Which is the smallest side of the triangle?

Solution 7

 

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

n the given figure, ∠QPR = 50o and ∠PQR = 60o. Show that :

a. PN < RN

b. SN < SR

 

 

Solution 18

 

 

Question 19

In ABC, BC produced to D, such that, AC = CD; ∠BAD = 125o and ∠ACD = 105o. Show that BC > CD.

Solution 19

 

Question 20

In PQR, PSQR ; prove that:

PQ > QS and PQ > PS

Solution 20

 

Question 21

In PQR, PS QR ; prove that:

PR > PS

Solution 21

 

Question 22

In PQR, PS QR ; prove that:

PQ + PR > QR and PQ + QR >2PS.

Solution 22

 

Question 23

In the given figure, T is a point on the side PR of triangle PQR. Show that

a. PT < QT

b. RT < QT

Solution 23

 

Question 24

In PQR is a triangle and S is any point in its interior. Prove that SQ + SR < PQ + PR.

Solution 24

 

 

Question 25

Prove that in an isosceles triangle any of its equal sides is greater than the straight line joining the vertex to any point on the base of the triangle.

Solution 25

 

 

Question 26

ABC in a isosceles triangle with AB = AC. D is a point on BC produced. ED intersects AB at E and AC at F. Prove that AF > AE.

Solution 26

 

Question 27

In ABC, AE is the bisector of ∠BAC. D is a point on AC such that AB = AD. Prove that BE = DE and ∠ABD > ∠C.

Solution 27

 

Question 28

In ABC, D is a point in the interior of the triangle. Prove that DB + DC < AB + AC.

Solution 28

 

 

Key Features of Study Materials for ICSE Class 9 Maths:

  • Include video lessons, question bank and solved sample papers
  • Designed according to the latest ICSE syllabus
  • Developed by subject experts
  • Content revised from time to time
  • Helpful when doing quick revision
  • Guidance when doing homework
  • Understand concepts easily
  • Significantly improve your Mathematics score