Question

how to prove Pythagoras theorm?

Answer 1

Pythagoras Theorem is applicable in case of triangles.
This theorem is based on the three sides of a triangle.
The Base, The perpendicular and The Hypotenuse.

It is put forward in a formula manner,
BASE² + PERPENDICULAR² = HYPOTENUSE²

Answer 2

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ANSWER:

Statement:

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

Given:

ABC is a triangle in which ∠ABC=90∘

Construction:

Draw BD⊥AC.

Proof:

In △ADB and △ABC

∠A=∠A              [Common angle]

∠ADB=∠ABC      [Each 90∘]

△ADB∼△ABC    [A−A Criteria]

So, ABAD=ACAB

Now, AB^2=AD×AC             ..........(1)

Similarly,

BC^2=CD×AC               ..........(2)

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

AB^2+BC^2=AD×AC+CD×AC

=AC(AD+CD)

=AC×AC

∴AB^2+BC^2=AC^2 

HENCE PROVED.

( Refer the attached pic )

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