FRANK Solutions for Class 9 Maths Chapter 13 - Inequalities in Triangles

How to show that the perimeter of a given triangle is more than the sum of its medians? Find answers in TopperLearning’s Frank solutions for ICSE Class 9 Mathematics Chapter 13 Inequalities in Triangles. Revise the application of properties of triangles to provide proofs in answers such as a particular side of an isosceles triangle is greater than another side.

Revise the Exterior Angle property, Angle Sum property and carious other properties of the triangle with our Frank textbook solutions. Practice makes you perfect; and that is why ICSE Class 9 Maths videos, online practice tests, and more study aids are at available on TopperLearning.

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Chapter 13 - Inequalities in Triangles Exercise Ex. 13.1

Question 1(a)

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

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesABC, = 56o, B = 64o and C = 60o.

Solution 1(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 1(b)

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

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesDEF, D = 32o, E = 56o and F = 92o.

Solution 1(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 1(c)

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

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesXYZ, X = 76o, Y = 84o.

Solution 1(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 2(a)

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

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesABC, A = 45o, B = 65o.

Solution 2(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 2(b)

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

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesDEF, D = 38o, E = 58o.

Solution 2(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 3
Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles
Solution 3
Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles
Question 4

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

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 4

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 5

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 5

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 6

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 6

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 7

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 7

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 8

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 8

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 9

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 9

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 10

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 10

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 11

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 11

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 12

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 12

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 13

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 13

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 14

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 14

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Question 15

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

a. PN < RN

b. SN < SR

 

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

 

Solution 15

 

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 16

In Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesABC, BC produced to D, such that, AC = CD; BAD = 125o and ACD = 105o. Show that BC > CD.

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 16

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 17(a)

In Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesPQR, PSFrank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesQR ; prove that:

PQ > QS and PQ > PS

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 17(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 17(b)

In Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesPQR, PSFrank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesQR ; prove that:

PR > PS

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 17(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 17(c)

In Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesPQR, PSFrank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesQR ; prove that:

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

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 17(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 18

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

a. PT < QT

b. RT < QT

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 18

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 19

In Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesPQR is a triangle and S is any point in its interior. Prove that SQ + SR < PQ + PR.Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 19

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

 

Question 20

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 20

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 21

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesABC 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.

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 21

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 22

In Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesABC, AE is the bisector of BAC. D is a point on AC such that AB = AD. Prove that BE = DE and ABD > C.

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 22

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Question 23

In Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In TrianglesABC, D is a point in the interior of the triangle. Prove that DB + DC < AB + AC.

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles

Solution 23

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles 

Frank Solutions Icse Class 9 Mathematics Chapter - Inequalities In Triangles