**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 + BC²**Construction: **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.

So, △ADB ~ △ABC,

Therefore,

⇒ BC^{2}= CD × AC ……………………..(2)

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

⇒ AB^{2} + BC^{2} = AD × AC + CD × AC

⇒AB^{2} + BC^{2} = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC^{2} = AB^{2} + BC^{2}

Hence, the Pythagorean theorem is proved.