#### Chapters

Chapter 2 - Exponents of Real Numbers

Chapter 3 - Rationalisation

Chapter 4 - Algebraic Identities

Chapter 5 - Factorisation of Algebraic Expressions

Chapter 6 - Factorisation of Polynomials

Chapter 7 - Introduction to Euclid’s Geometry

Chapter 8 - Lines and Angles

Chapter 9 - Triangle and its Angles

Chapter 10 - Congruent Triangles

Chapter 11 - Co-ordinate Geometry

Chapter 12 - Heron’s Formula

Chapter 13 - Linear Equations in Two Variables

Chapter 14 - Quadrilaterals

Chapter 15 - Areas of Parallelograms and Triangles

Chapter 16 - Circles

Chapter 17 - Constructions

Chapter 18 - Surface Areas and Volume of a Cuboid and Cube

Chapter 19 - Surface Areas and Volume of a Circular Cylinder

Chapter 20 - Surface Areas and Volume of A Right Circular Cone

Chapter 21 - Surface Areas and Volume of a Sphere

Chapter 22 - Tabular Representation of Statistical Data

Chapter 23 - Graphical Representation of Statistical Data

Chapter 24 - Measures of Central Tendency

Chapter 25 - Probability

## Chapter 9 - Triangle and its Angles

#### Pages 9 - 10

In a ΔABC, if ∠A = 55°, ∠B = 40°, find ∠C.

If the angles of a triangle are in the ratio 1: 2 : 3, determine three angles.

The angles of a triangle are (x − 40)°, (x − 20)° and `(1/2x-10)^@.` find the value of x

The angles of a triangle are arranged in ascending order of magnitude. If the difference

between two consecutive angles is 10°, find the three angles.

Two angles of a triangle are equal and the third angle is greater than each of those angles

by 30°. Determine all the angles of the triangle.

If one angle of a triangle is equal to the sum of the other two, show that the triangle is a

right triangle.

ABC is a triangle in which ∠A — 72°, the internal bisectors of angles B and C meet in O.

Find the magnitude of ∠BOC.

The bisectors of base angles of a triangle cannot enclose a right angle in any case.

If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.

In a ΔABC, ∠ABC = ∠ACB and the bisectors of ∠ABC and ∠ACB intersect at O such that ∠BOC = 120°. Show that ∠A = ∠B = ∠C = 60°.

Can a triangle have two right angles? Justify your answer in case.

Can a triangle have two obtuse angles? Justify your answer in case.

Can a triangle have two acute angles?Justify your answer in case.

Can a triangle have All angles more than 60°? Justify your answer in case.

Can a triangle have All angles less than 60° Justify your answer in case.

Can a triangle have All angles equal to 60°? Justify your answer in case.

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

#### Page 0

Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.

BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.

#### Page 0

In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.

In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.

In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.

In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC.

Find the measure of each exterior angle of an equilateral triangle.

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.

In Fig. 10.25, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD.

Determine the measure of each of the equal angles of a right-angled isosceles triangle.

OR

ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB.

#### Page 0

In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT.

In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP

respectively. Prove that LN = MN.

#### Page 0

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

#### Page 0

In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC

#### Textbook solutions for Class 9

## RD Sharma solutions for Class 9 Mathematics chapter 9 - Triangle and its Angles

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Concepts covered in Class 9 Mathematics chapter 9 Triangle and its Angles are Inequalities in a Triangle, Some More Criteria for Congruence of Triangles, Properties of a Triangle, Criteria for Congruence of Triangles, Congruence of Triangles, Concept of Triangles.

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