Question

Prove "Pythagoras Theorem"

Answer 1

✌️✌️ hey frnds......


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→Given :- We are given a right triangle ABC right angled at B .


→ Prove that :- AC² = AB² + BC²

→ Construction :- We draw BD perpendicular on AC .

→ Proof:- ∆ADB ≈ ∆ABC

So, AD/AB = AB/AC ..

or AD . AC = AB² .......(1)

Also,. ∆ BDC ≈ ∆ABC

So, CD/BC = BC/AC

or CD . AC = BC² .......(2)


Adding (1) & (2) ,


AD . AC + CD . AC = AB² + BC²


or , AC (AD + CD ) = AB² + BC²

or, AC . AC = AB² + BC²

or,. AC² = AB² + BC² .....


Hence, it is proved ....


I hope it's helpful ☺️☺️✅

Answer 2

heya!

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Prove "Pythagoras Theorem"

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so in this  "Pythagoras Theorem" we usually use the formula,

a²+b²=c²

hypotenuse is the line opposite to right angle and is the biggest of all sides

but this is to inform you that "Pythagoras Theorem" can only be used in right angle triangle .

now lets prove it

in this Δabc,

bd is the altitude

a and c are the sides

ac is the base

let ab = 5 , cb = 5 and b is 8

we have to find   bd

so here we use pythogoras theorm

since whole ac is 8

ad/cd = 8/2 = 4cm

now

a² +b²+=c²

c is the hypotneuse

4² + bd² = 5²

16 +bd² = 25

bd² = 25-16

bd² =9

bd=√9

bd=3cm

so the altitude bd is 3cm

in this way we have proved the pythogoras theoram

hope it helps u

:)