Activity › Discussion › Math › Math › Reply To: Math

::
Pythagoras theorem states that “The square of the hypotenuse side is equal to the sum of squares of the other two sides in a rightangle triangle“. The longest side of the rightangle 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 rightangle 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.