NCERT Solutions for Class 10 Maths Chapter 6 Triangles | Monster Thinks - Monster Thinks

# NCERT Solutions for Class 10 Maths Chapter 6 Triangles ### NCERT Solutions for Class 10 Maths Chapter 6 Triangles

NCERT Solutions for Class 10 Maths are solved by experts of MonsterThinks.in order to help students to obtain excellent marks in their board examination. All the questions and answers in the CBSE NCERT Books have been included on this page. We have provided all the Class 10 Maths NCERT Solutions with a detailed explanation i.e., we have solved all the questions with step-by-step solutions in understandable language. So students having excellent knowledge of NCERT Solutions Class 10 Maths can easily make a grade in their board exams. Read on to find out more about  NCERT Solutions for Class 10 Mathematics.

With the aim of imbibing skills and hard work among the students, the 10th class maths NCERT solutions have been designed. It contains previous years’ questions along with answers except those which are not included in the CBSE 10 maths syllabus.

CBSE NCERT solutions for class 10 maths will help the students acquire good practice to do their CBSE Class 10th exam confidently

### NCERT Solutions for Class 10 Maths Chapter 6 Triangles

Triangles Class 10 has a total of six exercises consisting of 64 Problems. The Questions are based on properties of triangles and 9 important theorems which are important in scoring good marks in CBSE Class 10 Exams.

### 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's Theorem and its Converse

(i) If a 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
AC2 = AB2 + BC2 (iii) Converse of Pythagoras Theorem: If in a triangle, the 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 Class 10 Triangles NCERT Solutions or save the solution images and take the printout to keep it handy for your exam preparation.