Question

Pythagoras theorem in SOLve

Answer 1

Hiii......

Consider a triangle ABC with BD as altitude.

Now,

tri.ADB ~ tri. ABC

So,
AD/AB = AB/AC

=> AD × AC = AB^2........... (1)

Also,

Tri. BDC ~ Tri. ABC

So,

CD/BC = BC/AC

=> CD × AC = BC^2............ (2)

Now, Add (1) & (2),

AD × AC + CD× AC = AB^2 + BC^2

=> AC (AD + CD) = AB^2 + BC^2

=> AC × AC = AB^2 + BC^2

=> AC^2 = AB^2 + BC^2....... ( HENCE PROVED )

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Answer 2

Consider a triangle ABC with BD as altitude.

Now,

tri.ADB ~ tri. ABC

So,

AD/AB = AB/AC

=> AD × AC = AB^2........... (1)

Also,

Tri. BDC ~ Tri. ABC

So,

CD/BC = BC/AC

=> CD × AC = BC^2............ (2)

Now, Add (1) & (2),

AD × AC + CD× AC = AB^2 + BC^2

=> AC (AD + CD) = AB^2 + BC^2

=> AC × AC = AB^2 + BC^2

=> AC^2 = AB^2 + BC^2....... ( HENCE PROVED )