Question

can someone give me the proof of Pythagoras theorem ​

Answer 1

Answer:

$\textbf{\huge{ Sure Friend! }}$

Step-by-step explanation:

Thank you

Answer 2

Answer:

Here i'm giving hope it would help you

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Step-by-step explanation:

Pythagoras Theorem 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“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

Pythagoras Theorem Formula

Consider the triangle given above:

Where “a” is the perpendicular side,

“b” is the base,

“c” is the hypotenuse side.

According to the definition, the Pythagoras Theorem formula is given as:

Hypotenuse^2 = Perpendicular^2 + Base^2  

c^2 = a^2 + b^2  

Pythagoras Theorem Proof

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

To Prove- AC^2 = AB^2 + BC^2

Construction: Draw a perpendicular BD meeting AC at D.

Proof:

We know, △ADB ~ △ABC

Therefore, △DAB=△BAC (corresponding sides of similar triangles)

Or, AB^2 = AD × AC ……………………………..……..(1)

Also, △BDC ~△ABC

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

Or, BC^2= CD × AC ……………………………………..(2)

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

AB^2 + BC^2 = AD × AC + CD × AC

AB^2 + BC^2 = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC^2 = AB^2 + BC^2

Hence, the Pythagorean theorem is proved.

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