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:

ABC, = 56o, B = 64o and C = 60o.

Solution 1(a)

  

Question 1(b)

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

 DEF, D = 32o, E = 56o and F = 92o.

Solution 1(b)

Question 1(c)

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

 XYZ, X = 76o, Y = 84o.

Solution 1(c)

  

Question 2(a)

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

 ABC, A = 45o, B = 65o.

Solution 2(a)

Question 2(b)

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

 DEF, D = 38o, E = 58o.

Solution 2(b)

Question 3
Solution 3
Question 4

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

Solution 4

  

Question 5

Solution 5

Question 6

Solution 6

Question 7

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

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

a. PN < RN

b. SN < SR

 

 

Solution 15

 

  

Question 16

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

Solution 16

  

Question 17(a)

In  PQR, PSQR ; prove that:

PQ > QS and PQ > PS

Solution 17(a)

  

Question 17(b)

In  PQR, PS QR ; prove that:

PR > PS

Solution 17(b)

  

Question 17(c)

In  PQR, PS QR ; prove that:

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

Solution 17(c)

  

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

Solution 18

  

Question 19

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

Solution 19

  

 

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

  

  

Question 21

 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 21

  

Question 22

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 22

  

Question 23

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

Solution 23