Question

In a right triangle the square of the hypotenuse is equal to the sum of the square of the other sides. This is a statement. which is the this statement Theorm

Answer 1

In mathematics, the Pythagoreantheorem, also known as Pythagoras'theorem, is a fundamental relation in Euclidean geometry among the threesides of a right triangle. It states that the square of the hypotenuse (the sideopposite the right angle) is equal to the sum of the squares of the othertwo sides.
The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":

a^{2}+b^{2}=c^{2},

where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.

Answer 2

Answer:

Given :

A right triangle ABC right angled at B.

To prove :

AC² = AB² + BC²

Construction :

Draw BD ⊥ AC

Proof :

In Δ ADB and Δ ABC

∠ A = ∠ A    [ Common angle ]

∠ ADB = ∠ ABC   [ Both are 90° ]

∴  Δ  ADB  Similar to Δ ABC   [ By AA similarity ]

So , AD / AB = AB / AC   [ Sides are proportional ]

= > AB² = AD . AC  ... ( i )

Now in Δ BDC and Δ ABC

∠ C = ∠ C    [ Common angle ]

∠ BDC = ∠ ABC   [ Both are 90° ]

∴  Δ  BDC Similar to Δ ABC   [ By AA similarity ]

So , CD / BC = BC / AC

= > BC² = CD . AC   ... ( ii )

Now adding both equation :

AB² + BC² = CD . AC +  AD . AC

AB² + BC² = AC ( CD + AD )

AB² + BC² = AC² .

AC² = AB² + BC² .

Hence proved .