Math, asked by h0arinmkomdiw, 1 year ago

State and prove pythagoras theorem

Answers

Answered by Anonymous
2

Pythagorean Theorem

The theorem states that:

"The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs" 


This theorem is talking about the area of the squares that are built on each side of the right triangle. 

Accordingly, we obtain the following areas for the squares, where the green and blue squares are on the legs of the right triangle and the red square is on the hypotenuse.( lets imagine that there be 3 squares of colours red blue and green)



area of the green square is a^2
area of the blue square is b^2
area of the red square is c^2 



From our theorem, we have the following relationship:

area of green square + area of blue square = area of red square or

a^2+b^2=c^2

hence proved



Answered by Anonymous
0

Step-by-step explanation:

Pythagoras' theorem :-

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

Step-by-step explanation:

It's prove :-

➡ Given :-

→ A △ABC in which ∠ABC = 90° .

➡To prove :-

→ AC² = AB² + BC² .

➡ Construction :-

→ Draw BD ⊥ AC .

➡ Proof :-

In △ADB and △ABC , we have

∠A = ∠A ( common ) .

∠ADB = ∠ABC [ each equal to 90° ] .

∴ △ADB ∼ △ABC [ By AA-similarity ] .

⇒ AD/AB = AB/AC .

⇒ AB² = AD × AC ............(1) .

In △BDC and △ABC , we have

∠C = ∠C ( common ) .

∠BDC = ∠ABC [ each equal to 90° ] .

∴ △BDC ∼ △ABC [ By AA-similarity ] .

⇒ DC/BC = BC/AC .

⇒ BC² = DC × AC. ............(2) .

Add in equation (1) and (2) , we get

⇒ AB² + BC² = AD × AC + DC × AC .

⇒ AB² + BC² = AC( AD + DC ) .

⇒ AB² + BC² = AC × AC .

 \huge \green{ \boxed{ \sf \therefore AC^2 = AB^2 + BC^2 }}

Hence, it is proved.

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