NCERT Solutions for Class 10 Maths Chapter 6: Triangles

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The NCERT Solutions for class 10 maths chapter 6 Triangles are provided in the article below. A triangle is a polygon having three sides and three angles. Based on whether they have equal sides or not, triangles can be categorised as equilateral, isosceles and scalene triangles.

Chapter 6 Triangles is included in the class 10 syllabus 2022-23 under the Unit Geometry. This unit carries a weightage of 15 Marks in class 10 mathematics board exam. Chapter 10 Circles is also a part of this unit. The important topics from this chapter includes similarity of triangles, congruence of triangles and pythagoras theorem.

NCERT Solutions for Class 10 Maths Chapter 6

Class 10 Maths Chapter 6 Triangles: Important Topics

Some important concepts of chapter 6 Triangles are given below:

Similarity of Triangles – Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are in the same ratio. Triangles with equal corresponding angles are called equiangular triangles.

Basic Proportionality Theorem states that the ratio of any two corresponding sides in two equiangular triangles is always the same.

Congruence of Triangles – Two triangles are said to be congruent if all their corresponding sides and angles are equal in measure.

Congruent triangles always satisfy any of the given conditions:

SSS (Side-Side-Side) Rule, SAS (Side-Angle-Side) Rule, ASA (Angle-Side-Angle) Rule, AAS (Angle-Angle-Side Rule), RHS (Right angle-Hypotenuse-Side) Rule.

Pythagoras Theorem – It states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of other two sides.

Pythagoras theorem can be represented as (H)² = (P)² + (B)², where H is Hypotenuse, P is perpendicular and B is Base.

NCERT Solutions for Class 10 Maths Chapter 6 Exercises:

The NCERT solutions of all the exercises of class 10 maths chapter 6 Triangles are given below:

Read Also:

Triangles Important Questions	Triangles Revision Notes	MCQ on Triangles
Tangent to a Circle	Circles MCQ	Cyclic Quadrilateral
Circles Revision Notes	Semicircles	Important Questions on Circles

Study Materials for Class 10 Maths:

Algebra	Mensuration Formula	Geometry
Number System	Math Study Material	Important Formulas in Maths

CBSE X Related Questions

1.
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :
Length (in mm)
Number of leaves
118 - 126
3
127 - 135
5
136 - 144
9
145 - 153
12
154 - 162
5
163 - 171
4
172 - 180
2
Find the median length of the leaves.
(Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5.)

Length (in mm)	Number of leaves
118 - 126	3
127 - 135	5
136 - 144	9
145 - 153	12
154 - 162	5
163 - 171	4
172 - 180	2

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2.
Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).

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3.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

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4.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

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5.
Solve the following pair of linear equations by the substitution method.
(i) x + y = 14
x – y = 4
(ii) s – t = 3
  \(\frac{s}{3} + \frac{t}{2}\) =6
(iii) 3x – y = 3
9x – 3y = 9
(iv) 0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3
(v)\(\sqrt2x\) + \(\sqrt3y\)=0
  \(\sqrt3x\) - \(\sqrt8y\) = 0
(vi) \(\frac{3x}{2} - \frac{5y}{3}\) =-2,
  \(\frac{ x}{3} + \frac{y}{2}\) = \(\frac{ 13}{6}\)

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6.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

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Triangles Important Questions: Important Similarity Concepts

Congruence Of Triangles: Conditions (SSS, SAS, ASA, RHS)

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NCERT Solutions for Class 10 Maths Chapter 6: Triangles

NCERT Solutions for Class 10 Maths Chapter 6

Class 10 Maths Chapter 6 Triangles: Important Topics

NCERT Solutions for Class 10 Maths Chapter 6 Exercises:

CBSE X Related Questions

2.
Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).

3.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

4.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

6.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

Similar Mathematics Concepts

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NCERT Solutions for Class 10 Maths Chapter 6: Triangles

NCERT Solutions for Class 10 Maths Chapter 6

Class 10 Maths Chapter 6 Triangles: Important Topics

NCERT Solutions for Class 10 Maths Chapter 6 Exercises:

CBSE X Related Questions

2. Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).

3. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

4. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

6. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

2.
Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).

3.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

4.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

6.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.