Asked/Added Questions From NCERT:

 ABC is a right angle triangle at B and BD is a perpendicular from B on to AC, the diagonal.

Triangles ABC and BDC are similar, as:

     . angle DBC = 90 - angle C = angle A

     . angle ABC = angle BDC = 90

Ratios of corresponding sides are equal.

     AB / BD = BC / DC = AC / BC

    So we get  BC² = AC * DC     --- (1)

Triangle ABC amd ADB are similar, as:

    . angle DBA = 90 - (90 - C) = angle C

    . angle ABC = 90 = angle ADB

so ratios of corresponding sides are equal

         AB / AD = BC / BD = AC / AB 

       So we get  AB² = AD * AC  --- (2)

  Add (1) and (2) to get:

       AB² + BC² = AC * ( AD + DC) = AC * AC = AC²

So the theorem is proved.