Question

Pythagoras theorem with formula and proof

Answer 1

Pythagoras theorem 

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

$A{C}^2=A{B}^2+B{C}^2$

 Proof 

We know, △ADB ~ △ABC

Therefore, $\frac{AD}{AB}=\frac{AB}{AC}$(corresponding sides of similar triangles)

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

Also, △BDC ~△ABC

Therefore, $\frac{CD}{BC}=\frac{BC}{AC}$ (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.

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