question_answer

Prove that the ratio of the areas of similar triangles is equal to the ratio of the squares on the corresponding sides.  

Answer:

Given Two triangles and  such that To prove Construction Draw  and (1/2) Proof Since, similar triangles are equiangular and their corresponding sides are proportional. Therefore,                 and                               ?(i)(1) Thus, in and                              [each 90°]                                       [from Eq. (i)] By AA similarity,                                                  ?(ii)(1) From Eqs. (i) and (ii), we get                                ?(ii) Now,                   (1/2) [Area of triangle  Base  Altitude]           [FromEq. (ii)] (1/2)                                     ?(iii) But         [by similarity of and]                              ?(iv)(1/2) From Eqs. (iii) and (iv), we get Hence proved.