Question

explain Pythagoras theorem with diagram

Answer 1

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Answer 2

$\huge{\bold{\red{Heya!!!}}}$


$\bold{\blue{Here\:is\:your\: answer\: }}$


Dear Student!

Here is the answer to your query.

 



 

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

 

Cheers!