# 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.

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## 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, PS QR ; 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:

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