Question

Prove that in a right angled triangle the square on this hypotenuse us to the sum of the square on the other two sides​

Answer 1

Pythagoras property is answer.

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Answer 2

Step-by-step explanation:

In Δ ADB and Δ ABC,

⇒ ∠ ADB = ∠ ABC

⇒ ∠ BAD = ∠ CAB

Δ ADB ~ Δ ABC (By AA similarity criterion)

Now,

AD/AB = AB/AC (corresponding sides are proportional)

AB² = AD * AC … (i)

Similarly, Δ BDC ~ Δ ABC

⇒ BC² = CD * AC … (ii)

Adding (i) and (ii)

⇒ AB² + BC² = (AD * AC) + (CD * AC)

⇒ AB² + BC² = AC * (AD + CD)

⇒ AB² + BC² = AC²

Hence Proved.

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