Get Free **NCERT Solutions for Class 10 Maths Chapter 6** Ex 6.1 PDF. Triangles Class 10 Maths NCERT Solutions are extremely helpful while doing your homework. Exercise 6.1 Class 10 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 6 **Maths Class 10 Triangles** Exercise 6.1 provided in NCERT TextBook.

**Topics and Sub Topics in Class 10 Maths Chapter 6 Triangles:**

Section Name | Topic Name |

6 | Triangles |

6.1 | Introduction |

6.2 | Similar Figures |

6.3 | Similarity Of Triangles |

6.4 | Criteria For Similarity Of Triangles |

6.5 | Areas Of Similar Triangles |

6.6 | Pythagoras Theorem |

6.7 | Summary |

- Triangles Class 10 Ex 6.1
- Triangles Class 10 Ex 6.2
- Triangles Class 10 Ex 6.3
- Triangles Class 10 Ex 6.4
- Triangles Class 10 Ex 6.5
- Triangles Class 10 Ex 6.6
- Extra Questions for Class 10 Maths Triangles

## NCERT Solutions For Class 10 Maths Chapter 6 Triangles Ex 6.1

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex Ex 6.1 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercise 6.1

Board | CBSE |

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 6 |

Chapter Name | Triangles |

Exercise | Ex 6.1 |

Number of Questions Solved | 3 |

Category | NCERT Solutions |

Question 1.

Fill in the blanks by using the correct word given in brackets.

(i) All circles are ……………. . (congruent/similar)

(ii) All squares are …………… . (similar/congruent)

(iii) All …………….. triangles are similar. (isosceles/equilateral)

(iv) Two polygons of the same number of sides are similar, if

(a) their corresponding angles are …………… and

(b) their corresponding sides are …………… (equal/proportional)

Solution:

Question 2.

Give two different examples of pair of

(i) similar figures.

(ii) non-similar figures.

Solution:

### Class 10 Maths Triangles Mind Map

#### Similar Figures

Two figures having the same shape but not necessarily the same size are called similar figures

Two figures having the same shape as well as same size are called congruent figures

Note that all congruent figures are similar but the similar figures need not be congruent.

#### Similarity of Polygons

Two polygons of the same number of sides are similar if

(i) their corresponding angles are equal and

(ii) their corresponding sides are in the same ratio (or proportion)

#### Similarity of Triangles

Two triangles are similar if

(i) their corresponding angles are equal and

(ii) their corresponding sides are in the same ratio (or proportion)

Note : If the corresponding angles of two triangles are equal, then they are known as equiangular triangles.

The ratio of any two corresponding sides in two equiangular triangles is always the same.

#### Basic Proportionality Theorem (BPT) and its Converse

Basic Proportionality Theorem

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then other two sides are divided in the same ratio. Thus in ∆ABC, if DE || BC, then

Converse of BPT

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side,

#### Criteria For Similarity of Triangles

(i) AAA Similarity Criterion : If in two triangles, corresponding angles are equal then their corresponding sides are in the same ratio and hence the two triangles are similar.

(ii) AA Similarity Criterion : If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.

(iii) SSS Similarity Criterion : If in two triangles, corresponding sides are in the same ratio then their corresponding angles are equal and hence the triangles are similar.

(iv) SAS Similarity Criterion : If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportion), then the two triangles are similar.

#### Areas of Similar Triangles

The ratio of the area of two similar triangles is equal to the ratio of the squares for their corresponding sides thus if ∆ABC – ∆PQR, then

#### Pythagoras Theorem and its Converse

(i) If perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then the triangles on both sides of the perpendicular are similar to the whole triangle and also to each other.

(ii) Pythagoras Theorem : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Thus in right ∆ABC right angled at B

AC^{2} = AB^{2} + BC^{2}

(iii) Converse of Pythagoras Theorem : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

You can also download the free **PDF of Ex 6.1 Class 10 Triangles NCERT Solutions** or save the solution images and take the print out to keep it handy for your exam preparation.

Download NCERT Solutions For Class 10 Maths Chapter 6 Triangles PDF

Question 3.

State whether the following quadrilaterals are similar or not.

Solution:

**More Resources for CBSE Class 10**

- NCERT Solutions
- NCERT Solutions for Class 10 Maths
- NCERT Solutions for Class 10 Science
- NCERT Solutions for Class 10 Social
- NCERT Solutions for Class 10 English
- NCERT Solutions for Class 10 Hindi
- NCERT Solutions for Class 10 Sanskrit
- NCERT Solutions for Class 10 Foundation of IT
- RD Sharma Class 10 Solutions

Formulae Handbook for Class 10 Maths and Science

### NCERT Solutions for Class 10 Maths

- Chapter 1 Real Numbers
- Chapter 2 Polynomials
- Chapter 3 Pair of Linear Equations in Two Variables
- Chapter 4 Quadratic Equations
- Chapter 5 Arithmetic Progressions
- Chapter 6 Triangles
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction to Trigonometry
- Chapter 9 Some Applications of Trigonometry
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Areas Related to Circles
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability

We hope the NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.1, help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercise 6.1, drop a comment below and we will get back to you at the earliest.

Susheel Kumar Patel says

December 13, 2018 at 12:11 pmit is helpful for every student . great thankful for this solution .