Pythagoras theorem states that “The square of the hypotenuse side is equal to the sum of squares of the other two sides in a right-angle triangle“. The longest side of the right-angle triangle is called the hypotenuse. Because it is opposite to the angle of 90 degrees. The other two sides are perpendicular and base.
Let us consider the right-angle triangle ABC with 90 degrees at B and draw a perpendicular BD meeting AC at D as shown in the photo.
According to the question: △ADB ~ △ABC
Therefore, AD/AB=AB/AC (corresponding sides of similar triangles)
Or, AB^2 = AD × AC ……………………………..……..(1)
Also, △BDC ~△ABC
Therefore, CD/BC=BC/AC (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 Pythagoras theorem is proved.