Math, asked by kshitijnimje4432, 10 months ago

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Answers

Answered by Anonymous
4

Answer:

Given :

A right triangle ABC right angled at B.

To prove :

AC² = AB² + BC²

Construction :

Draw BD ⊥ AC

Proof :

In Δ ADB and Δ ABC

∠ A = ∠ A    [ Common angle ]

∠ ADB = ∠ ABC   [ Both are 90° ]

∴  Δ  ADB  Similar to Δ ABC   [ By AA similarity ]

So , AD / AB = AB / AC   [ Sides are proportional ]

= > AB² = AD . AC  ... ( i )

Now in Δ BDC and Δ ABC

∠ C = ∠ C    [ Common angle ]

∠ BDC = ∠ ABC   [ Both are 90° ]

∴  Δ  BDC Similar to Δ ABC   [ By AA similarity ]

So , CD / BC = BC / AC

= > BC² = CD . AC   ... ( ii )

Now adding both equation :

AB² + BC² = CD . AC +  AD . AC

AB² + BC² = AC ( CD + AD )

AB² + BC² = AC² .

AC² = AB² + BC² .

Hence proved .

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Answered by XxMissPaglixX
15

ʜᴏᴘᴇ ʏᴏᴜ ɢᴏᴛ ᴜʀ ᴀɴsᴡᴇʀ

❤ᴛʜᴀɴᴋ ʏᴏᴜ❤

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