Question

Explain Pythagoras theorem

Answer 1

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

Answer 2

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. .......