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

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

Question 1

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

ABC, ∠ = 56

^{o}, ∠B = 64^{o}and ∠C = 60^{o}.
Solution 1

Question 2

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

DEF, ∠D
= 32

^{o}, ∠E = 56^{o }and ∠F = 92^{o}.
Solution 2

Question 3

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

XYZ, ∠X
= 76

^{o}, ∠Y = 84^{o}.
Solution 3

Question 4

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

ABC, ∠A
= 45

^{o}, ∠B = 65^{o}.
Solution 4

Question 5

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

DEF, ∠D
= 38

^{o}, ∠E = 58^{o}.
Solution 5

Question 6

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

Solution 6

Question 7

n the given figure, ∠QPR = 50

^{o}and ∠PQR = 60^{o}. Show that :
a. PN < RN

b. SN < SR

Solution 7

Question 8

In ABC, BC produced to D, such that, AC = CD; ∠BAD
= 125

^{o}and ∠ACD = 105^{o}. Show that BC > CD.
Solution 8

Question 9

In PQR, PSQR ; prove that:

PQ > QS and PQ > PS

Solution 9

Question 10

In
PQR, PSQR ; prove that:

PR
> PS

Solution 10

Question 11

In
PQR, PSQR ; prove that:

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

Solution 11

Question 12

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

a.
PT < QT

b.
RT < QT

Solution 12

Question 13

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

Solution 13

Question 14

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 14

Question 15

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 15

Question 16

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 16

Question 17

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

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

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