# 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.

## Chapter 13 - Inequalities in Triangles Exercise Ex. 13.1

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

ABC, ∠ = 56^{o}, ∠B = 64^{o} and ∠C = 60^{o}.

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

DEF, ∠D
= 32^{o}, ∠E = 56^{o }and ∠F
= 92^{o}.

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

XYZ, ∠X
= 76^{o}, ∠Y = 84^{o}.

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

ABC, ∠A
= 45^{o}, ∠B = 65^{o}.

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

DEF, ∠D
= 38^{o}, ∠E = 58^{o}.

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

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

a. PN < RN

b. SN < SR

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

In PQR, PSQR ; prove that:

PQ > QS and PQ > PS

In PQR, PSQR ; prove that:

PR > PS

In PQR, PSQR ; prove that:

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

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

a. PT < QT

b. RT < QT

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

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.

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.

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.

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

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