Pythagoras Theorem

Pythagoras Theorem. (B audhayan Theorem)

Theorem 8.3: - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given: -  is a right angle of 

To Prove:- 

Construction:- is drawn

Proof:- In 

Or, AB2 = AC X AD ---------------------(i)

Similarly 

Or, BC2 = AC X CD ---------------------(ii)

Adding (i) and (ii) we get

AB2 + BC2 = AC X AD + AC X CD

= AC X (AD + CD)

= AC X AC

= AC2

Or, AC2 = AB2 + BC2

Theorem 8.4 (Converse of Pythagoras Theorem): - In a triangle, if the 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.

Given:- In 

To prove:- 

Construction:- A triangle PQR is constructed such that PQ = AB, QR = BC and 

Proof:- In 

Or, PR2 = AB2 +BC2--------------(i) [PQ = AB, QR = BC]

But AC2 = AB2 + BC2 ------------(ii) (given)

Or, PR = AC

Or, 

Hence 

Example 13. Determine whether the triangle having sides (2a – 1) cm, and (2a + 1) cm is a right angled triangle.

Sol:- Let AB = (2a - 1) cm,

AC = (2a + 1) cm

is a right angled triangle.

___________________________________________________________

                          www.cbsekey.com

                          other usefull links

science| mathematics|sample Paper|solutions|social