CBSE Class 10 Answered

Pythagoras Theorem

Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

Given: A right triangle ABC right angled at B.

To prove: AC² = AB² + BC²

Construction: Draw BD AC

Proof :

We know that: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

ADB ABC

So, (Sides are proportional)

Or, AD.AC = AB² ... (1)

Also, BDC ABC

So,

Or, CD. AC = BC² ... (2)

Adding (1) and (2),

AD. AC + CD. AC = AB² + BC²

AC (AD + CD) = AB² + BC²

AC.AC = AB² + BC²

AC² = AB² + BC²

Hence Proved.

OR