Question

To get 50 points... heres the question
PROOF OF PYTHAGORAS THEOREM BY DIFFERENT METHODS
(AT LEAST 5 METHODS)
PLZ ITS URGENT...

Answer 1

Given : A right ΔABC right angled at B

To prove : AC2 = AB2 + BC2

 

Construction : Draw AD ⊥ AC

Proof : ΔABD and ΔABC

∠ADB = ∠ABC = 90°

∠BAD = ∠BAC  (common)

∴ ΔADB ∼ ΔABC  (by AA similarly criterion)



⇒ AD × AC = AB2    ...... (1)

 

Now In ΔBDC and ΔABC

∠BDC = ∠ABC = 90°

∠BCD = ∠BCA  (common)

∴ ΔBDC ∼ ΔABC  (by AA similarly criterion)



⇒ CD × AC = BC2    ........ (2)

 

Adding (1) and (2) we get

AB2 + BC2 = AD × AC + CD × AC

= AC (AD + CD)

= AC × AC = AC2

∴ AC2 = AB2 + BC2

Answer 2

Hey mate ^_^

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Answer:
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Given : A right ΔABC right angled at B

To prove : AC^2 = AB^2 + BC^2

 
Construction : Draw AD ⊥ AC

Proof : ΔABD and ΔABC

∠ADB = ∠ABC = 90°

∠BAD = ∠BAC  (common)

∴ ΔADB ∼ ΔABC  (by AA similarly criterion)

=> AD/AB = AB/AC

⇒ AD × AC = AB^2    ...... (1)

 
Now In ΔBDC and ΔABC

∠BDC = ∠ABC = 90°

∠BCD = ∠BCA  (common)

∴ ΔBDC ∼ ΔABC  (by AA similarly criterion)

=> CD/BC = BC/AC

⇒ CD × AC = BC^2    ........ (2)

 
Adding (1) and (2) we get

AB^2 + BC^2 = AD × AC + CD × AC

= AC (AD + CD)

= AC × AC = AC^2

∴ AC^2 = AB^2 + BC^2


#Be Brainly❤️