Question

Pythagoras theorem

Answer 1

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 Perpendicular, Base and Hypotenuse.

Pythagoras Theorem Proof

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,

\(\frac{AD}{AB} = \frac{AB}{AC}\)

(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.