# Class 7 Maths Chapter 6 Exercise 6.5 Pdf Notes NCERT Solutions

Class 7 Maths Chapter 6 The Triangles And Its Properties Exercise 6.5 pdf notes:-

**Exercise 6.5** Class 7 maths Chapter 6 Pdf Notes:-

**To see video Solution Of This Exercise Click Here**

## Ncert Solution for Class 7 Maths Chapter 6 The Triangles And Its Properties Exercise 6.5 Tips:

**THINK, DISCUSS AND WRITE**

Is the sum of any two angles of a triangle always greater than the third angle?

**RIGHT-ANGLED TRIANGLES AND PYTHAGORAS PROPERTY**

Pythagoras, a Greek philosopher of sixth century

B.C. is said to have found a very important and useful

property of right-angled triangles given in this section.

The property is, hence, named after him. In fact, this

property was known to people of many other

countries too. The Indian mathematician Baudhayan

has also given an equivalent form of this property.

We now try to explain the Pythagoras property.

In a right-angled triangle, the sides have some

special names. The side opposite to the right angle

is called the hypotenuse; the other two sides are

known as the legs of the right-angled triangle.

In ∆ABC, the right-angle is at B. So,

AC is the hypotenuse. AB and BC are the legs of

∆ABC.

Make eight identical copies of right angled

triangle of any size you prefer. For example, you

make a right-angled triangle whose hypotenuse is a

units long and the legs are of lengths b units and

c units Draw two identical squares on a sheet with sides

of lengths b + c.

You are to place four triangles in one square and the remaining four triangles in the

other square,

The squares are identical; the eight triangles inserted are also identical.

Hence the uncovered area of square A = Uncovered area of square B.

i.e., Area of inner square of square A = The total area of two uncovered squares in square B.

a2= b2+c2

This is Pythagoras property. It may be stated as follows:

In a right-angled triangle,

the square on the hypotenuse = sum of the squares on the legs.

Pythagoras property is a very useful tool in mathematics. It is formally proved as a

theorem in later classes. You should be clear about its meaning.

It says that for any right-angled triangle, the area of the square on the hypotenuse is

equal to the sum of the areas of the squares on the legs.

Draw a right triangle, preferably on

a square sheet, construct squares on

its sides, compute the area of these

squares and verify the theorem

practically

If you have a right-angled triangle,

the Pythagoras property holds. If the

Pythagoras property holds for some

triangle, will the triangle be right-

angled? (Such problems are known as

converse problems). We will try to

answer this. Now, we will show that,

if there is a triangle such that sum of

the squares on two of its sides is equal

to the square of the third side, it must

be a right-angled triangle.

**If the Pythagoras property holds, the triangle must be right-angled.**