Question

write and prove pythagores theorem​

Answer 1

Answer:

Statement :- Pythagoras theorem states that ;

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

Given :- A right-angled triangle ABC, right-angled at B.

To Prove :- AC2 = AB2 + BC2

Construction :- Draw a perpendicular BD meeting AC at D.

Proof :-

We know, △ADB ~ △ABC

Therefore, ADAB=ABAC (corresponding sides of similar triangles)

Or, AB2 = AD × AC ……………………………..……..(1)

Also, △BDC ~△ABC

Therefore, CDBC=BCAC (corresponding sides of similar triangles)

Or, BC2= CD × AC ……………………………………..(2)

Adding the equations (1) and (2) we get,

AB2 + BC2 = AD × AC + CD × AC

AB2 + BC2 = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC2 = AB2 + BC2

Hence, the Pythagorean theorem is proved.

( Note :- Pythagorean theorem is only applicable to Right-Angled triangle . )

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