# PYTHAGORAS THEOREM (TRIANGLES THEOREMS)

## Pythagoras Theorem or Pythagoras Theorem formula(Triangles Theorems class 10 maths)

There is total nine theorems in this chapter, in which **Pythagoras theorem ****6.8** or **Pythagoras theorem formula****,** * Converse of Pythagoras theorem 6.9* and

*etc. are frequently asked in board exams. GICSU*

**BPT theorem 6.1****Class 10th Maths Chapter 6 Triangles**India’s No. 1 handwritten (like class notes) complete explanation of accurate and easy proofs for all theorems covered in NCERT textbooks. You can easily download this PDF for free and start your preparation to get the maximum marks in all upcoming exams.

**Maths Theorems for 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 * Pythagoras Theorem Formula*,

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

**BPT theorem**

**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.

**Triangles Theorems for Class 10 Maths Proof: **

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**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.

**NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1**

**NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry of exercises 9.1** for all boards. We have updated all the contents for the new academic session 2021-2022.