Question

prove the Pythagoras theorm ​

Answer 1

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

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

see the attachment

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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