Question

Explain the Pythagorean Theorem, its proofs and applications.​

Answer 1

Pythagoras Theorem is an important topic in Maths, which explains the relation between the sides of a right-angled triangle.

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.

Applications of Pythagoras Theorem
To know if the triangle is a right-angled triangle or not.
In a right-angled triangle, we can calculate the length of any side if the other two sides are given.
To find the diagonal of a square.

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