Question

prove pythagoras theorm​

Answer 1

The proof of Pythagorean Theorem in mathematics is very important. In a right angle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. States that in a right triangle that, the square of a (a2) plus the square of b (b2) is equal to the square of c (c2

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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.

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