#### Chapters

Chapter 2: Profit , Loss and Discount

Chapter 3: Compound Interest

Chapter 4: Expansions

Chapter 5: Factorisation

Chapter 6: Changing the subject of a formula

Chapter 7: Linear Equations

Chapter 8: Simultaneous Linear Equations

Chapter 9: Indices

Chapter 10: Logarithms

Chapter 11: Triangles and their congruency

Chapter 12: Isosceles Triangle

Chapter 13: Inequalities in Triangles

Chapter 14: Constructions of Triangles

Chapter 15: Mid-point and Intercept Theorems

Chapter 16: Similarity

Chapter 17: Pythagoras Theorem

Chapter 18: Rectilinear Figures

Chapter 19: Quadrilaterals

Chapter 20: Constructions of Quadrilaterals

Chapter 21: Areas Theorems on Parallelograms

Chapter 22: Statistics

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Perimeter and Area

Chapter 25: Surface Areas and Volume of Solids

Chapter 26: Trigonometrical Ratios

Chapter 27: Trigonometrical Ratios of Standard Angles

Chapter 28: Coordinate Geometry

## Chapter 13: Inequalities in Triangles

### Frank solutions for Class 9 Maths ICSE Chapter 13 Inequalities in Triangles Exercise 13.1

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

ΔABC, ∠ = 56°, ∠B = 64° and ∠C = 60°.

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

ΔDEF, ∠D = 32°, ∠E = 56°^{ }and ∠F = 92°.

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

ΔXYZ, ∠X = 76°, ∠Y = 84°.

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

ΔABC, ∠A = 45°, ∠B = 65°.

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

ΔDEF, ∠D = 38°, ∠E = 58°.

Name the smallest angle in each of these triangles:

In ΔABC, AB = 6.2cm, BC = 5.6cm and AC = 4.2cm

Name the smallest angle in each of these triangles:

In ΔPQR, PQ = 8.3cm, QR = 5.4cm and PR = 7.2cm

Name the smallest angle in each of these triangles:

In ΔXYZ, XY = 6.2cm, XY = 6.8cm and YZ = 5cm

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

In ΔABC, the exterior ∠PBC > exterior ∠QCB. Prove that AB > AC.

ΔABC is isosceles with AB = AC. If BC is extended to D, then prove that AD > AB.

Prove that the perimeter of a triangle is greater than the sum of its three medians.

Prove that the hypotenuse is the longest side in a right-angled triangle.

D is a point on the side of the BC of ΔABC. Prove that the perimeter of ΔABC is greater than twice of AD.

For any quadrilateral, prove that its perimeter is greater than the sum of its diagonals.

ABCD is a quadrilateral in which the diagonals AC and BD intersect at O. Prove that AB + BC + CD + AD < 2(AC + BC).

In ABC, P, Q and R are points on AB, BC and AC respectively. Prove that AB + BC + AC > PQ + QR + PR.

In ΔPQR, PR > PQ and T is a point on PR such that PT = PQ. Prove that QR > TR.

ABCD is a trapezium. Prove that:

CD + DA + AB + BC > 2AC.

ABCD is a trapezium. Prove that:

CD + DA + AB > BC.

In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that : PN < RN

In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that: SN < SR

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

In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PQ > PS

In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PR > PS

In ΔPQR, PS ⊥ QR ; prove that: PQ + PR > QR and PQ + QR >2PS.

In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that PT < QT

In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that RT < QT

In ΔPQR 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.

ΔABC 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 ΔABC, AE is the bisector of ∠BAC. D is a point on AC such that AB = AD. Prove that BE = DE and ∠ABD > ∠C.

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

## Chapter 13: Inequalities in Triangles

## Frank solutions for Class 9 Maths ICSE chapter 13 - Inequalities in Triangles

Frank solutions for Class 9 Maths ICSE chapter 13 (Inequalities in Triangles) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Class 9 Maths ICSE solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Frank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Maths ICSE chapter 13 Inequalities in Triangles are If two sides of a triangle are unequal, the greater side has the greater angle opposite to it., If Two Angles of a Triangle Are Unequal, the Greater Angle Has the Greater Side Opposite to It., Of All the Lines, that Can Be Drawn to a Given Straight Line from a Given Point Outside It, the Perpendicular is the Shortest., Inequalities in a Triangle.

Using Frank Class 9 solutions Inequalities in Triangles exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Frank Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 9 prefer Frank Textbook Solutions to score more in exam.

Get the free view of chapter 13 Inequalities in Triangles Class 9 extra questions for Class 9 Maths ICSE and can use Shaalaa.com to keep it handy for your exam preparation