# Pythagoras theorem 6.8 Class 10

Pythagoras theorem Class 10 (also called Pythagorean Theorem) :

it states that : “In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides“.

Note: Here the sides of this triangle are named as Base, Perpendicular and Hypotenuse.

Here, the hypotenuse is the longest side, opposite to the angle 90⁰.

Given: A right triangle ABC in which B is right angle.

To Prove: AC² = AB² + BC²Construction: Draw a perpendicular line BD, which meets AC at D.

Proof:

By Theorem 6.7: If a perpendicular is drawn from the vertex of the right angle of the a right triangle to the hypotenuse then the triangle on both sides of the perpendicular are similar to the whole triangle and to each other.

Therefore,

⇒ BC2= CD × AC ……………………..(2)

Adding the equations (1) and (2) we get,

⇒ AB2 + BC2 = AD × AC + CD × AC

⇒AB2 + BC2 = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC2 = AB2 + BC2

Hence, the Pythagorean theorem is proved.