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:-
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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.
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