Class:VII

About Pythagoras

Pythagoras was born in the island of Samos in ancient Greece . There is no certainty regarding the exact year when he was born, but it is believed that it was around 570 BC That is about 2,570 years ago!

About Pythagoras(cont…)

At Croton he started a school which concentrated in the teaching and learning of Mathematics, Music, Philosophy, and Astronomy and their relationship with Religion.

He emphasized justice based on equality. Calmness and gentleness were principles encouraged at the school.

Lets study the Pythagoras Theorem

a2 b2 c2

hypotenuse

side

side

a

b

c

Let’s look how the theorem was derived

3cm

4cm

5cm

A

B C

D

E

F G

H

I

---------------

AREA OF A SQUARE AIHC= l x l =5 cm x 5cm = 25 sq cm

AREA OF A SQUARE BCGF = 4 cm X 4cm = 16sqcm

AREA OF A SQUARE DABE =3 cm X 3 cm = 9 sqcm

9sqcm

16sqcm

25sqcm

Therefore……In a right angled triangle , the area of the square on the hypotenuse is equal to the sum of areas of the squares on the remaining two sides.

(Hypotenuse)2 (side 1)2 (side 2)2

EXAMPLE…..The length of the sides forming the right angled of a right angled triangle are 6 m and 8 m . Find the hypotenuse.

6 m

8 m

?According to Pythagoras theorem ,

(Hypotenuse)2 = (side1)2 + (side2)2 = (6m)2 + (8 m)2 = 36sqm + 64sqm = 100sqmHypotenuse = (10 m)2(hypotenuse)2 = 100 m2Hypotenuse = 10m

15cm 9cm

?

In the alongside figure the hypotenuse and one side of the right angle is given . Find the length of the other side.

(hypotenuse)2 = (side1)2 + (side2)2(15 cm)2 = (9 cm)2 + (second side)2 225 sqcm= 81sqcm + (second side)2 225 sqcm – 81sqcm = (second side)2 144 sqcm = (second side)2 (12cm)2 = (second side)2

12cm = second side