Page 3 - LN
P. 3

u
                                           o
                                                                        e
                                                     e
                                                       q
                                           r
                                          f
                                                           i
                                                                      g
                                                         a
                                                           t

                                                 )
                                                 i
                                               (
                                                i


                                             m
                                                                         t
                                                   i
                                                   n
                                                            o

                                                                 ,
                                                                   w
                                                                    e

                                                               (

               Putting the value of       from (ii) in equation (i), we get,,
                                                                )
                                                                i
                                                             n


                                              o
                                                                           e
                                                                                      t
                                    o

                                               f
                                                                             s
                                                                               m

                                       a
                                         e
                                        r
                                                                                 e
                                                                              a

                                      f
                                           a
                                            s
                                                                                   a
                                                            t
                                                             r
                                                                    s
                                                                      i
                                                           r

                                                                   e
                                                                 g
                                                                  l
                                                              i
                                                              a
                                                                n
                                                          a
                                                                         h
                                                   o


                                                t
                                                 w
                                                                       s
                                                         i
                                                         l
                                                     si
                                                                         t
                                                       m
                            h
                                 t

                           t
                             e
                                  i

                    e
                      t
                        a

                          t
                               r
                                a
                                                                                          r

                       h
                   v

                                                                                                o
                                                                                              o
                                                                                       h
               P
               Prove that the ratio of areas of two similar triangles is the same as s the ratio of
                                                                                                 f

                 r
                                  o
                                                                                        e
                  o
                                                                                           a
                                                                                             i
                                                                                            t
                                                 n
                                                   g

                           s

                                                          a
                                                         i
                      u
               the squares of their corresponding median..
                                                           n
                   sq
                         r
                                                     m
                         e
                                                        d
                                                       e
                       a
                                              n
                                         e
                               t
                                       r
                                        r
                                   i
                                 e
                                h

                                     co
                                             o
                                          sp

                                                 i
                              f
                                   r
                                               d
                             o
               Given: Triangles ABC and DEF are similarr
               G i v e n :   T r i a n g l e s  A B C   a n d   D E F   a r e   si m i l a
               To prove:
               Proof:

                                          a
               Triangles ABC and DEF are similar.
                                           r
                    n
                     g
                                      E
                 r
                                        F


                  a
                                  d
               T
                  i
                          A
                                                    r

                                              s
                             C
                            B
                                                  l
                                                m
                                               i
                                                   a
                                                     .
                                            e
                                                  i
                      l
                                    D
                                 n

                        s
                       e
                                a
               Hence,
                                          (1)

                                           (
                                                  (2))
                                            2
                                                                   y
                                                                        S
                                                                         )
                                                                      A

                                                                     S
                                            n
                                             d

                                          a
                                                 E
                                                  Q

                                               D
                                 l
                                  e
               Therefore, triangles ABP and DEQ are similar (by SAS)..
                                g
                                       B
                                        P
                                   s
                                     A
                                                              a
                                                             l
                                                             i
                                                               r
                                                                 b
                                                                 (

                                                           m
                                                      r
                                                       e

                                                     a
                                                          i
                                                         s

               Thus,
               Hence,


                                                            3
   1   2   3