# NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.5

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**Class 10 Maths solutions****Class 10 Maths Chapter 6 Exercise 6.5**

*NCERT Solutions for Class 10 Maths Chapter 6 *Triangles of exercise 6.5 *(Class 10 Maths *Ex 6.5) for all boards. We **have updated all the contents for the new academic session 2021-2022.**

*NCERT Solutions for Class 10 Maths Chapter 6*Triangles of exercise 6.5

Get free **E****x 6.5 class 10 Maths****NCERT Solutions for Chapter 6 Triangles** India’s No. 1 Handwritten (Like Class Notes) which provides a complete explanation of the exact and easy solution to all the problems covered in NCERT textbooks to the students * class 10 Ex 6.5 Triangles *in PDF format, which is prepared by our subject qualified and experts in NCERT textbooks.

You can download this ** NCERT Maths class 10 PDF ** for free and start your preparation to get maximum marks in upcoming and Board examinations.

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**Maths Class 10 Chapter****6 exercise 6.5**PDF helps you in your preparation with exercise differentiation so that you can read each chapter more easily and can come back to any chapter again if necessary.

**NCERT Class 10th M****aths chapter 6 Ex 6.5 ** Pdf is Handwritten under the CBSE guidelines to help you score well in all upcoming exams.

### Math NCERT Solution Class 10

NCERT * Math Class 10*, Several important theorems are introduced which form the basis of mathematical concepts. Not only to score well in the board exams but also to build a strong foundation in the subject, it is necessary for the class 10 students to learn all the theorems thoroughly with statements and proofs. There are some important Theorem in NCERT Maths class 10 like

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**Pythagoras Theorem Formula**

**Converse of****Pythagoras,***etc. which is often asked in exams.*

**BPT theorem**

**NCERT Solutions for Class 10 Maths ex 6.5 Triangles**

**NCERT Solutions for Class 10 Maths ex 6.5 Triangles**

**List of Important Class 10 Maths Theorems**

* Basic Proportionality Theorem or BPT (Theorem 6.1)*: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

* Converse of BPT Theorem (Theorem 6.2):* If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

* Areas of Similar Triangles (Theorem 6.6): *The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

* Pythagoras Theorem (Theorem 6.8): *In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

* Converse of Pythagoras theorem (Theorem 6.9):* In a triangle, if 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.

**In this chapter you have studied the following points **

- If in two triangles, corresponding angles are equal, then their corresponding sides are in

the same ratio and hence the two triangles are similar (AAA 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 (AA 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 (SSS 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 (proportional), then the triangles are similar

(SAS similarity criterion).

**Important Points:**

- All the congruent figures are similar but the converse is not true.
- 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 (i.e., proportion). - 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 (i.e., proportion). - 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.