Question

Question :

=State and prove pythagoreus theorem ?

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Answer 1

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

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Answer 2

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, AD/AB = AB/AC

Now, AB² =AD×AC            

Similarly,

BC ² =CD×AC              

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

AB² + BC² = AD×AC+CD×AC

= AC (AD+CD)

= AC×AC

∴ AB² + BC ² = AC²  [henceproved]