6.  In Fig, \small AC=AE,AB=AD and \small \angle BAD= \angle EAC. Show that \small BC=DE.

                                  

Answers (1)

From the given figure following result can be drawn :-  

                     \angle BAD\ =\ \angle EAC

Adding \angle DAC to the both sides, we get :

                     \angle BAD\ +\ \angle DAC\ =\ \angle EAC\ +\ \angle DAC

                                               \angle BAC\ =\ \angle EAD

Now consider \Delta ABC  and   \Delta ADE ,    :-

  (i)               AC\ =\ AE                          (Given)

  (ii)   \angle BAC\ =\ \angle EAD                      (proved above)

 (iii)          AB\ =\ AD                              (Given)

Thus by SAS congruence we can say that :

                                           \Delta ABC\ \cong \ \Delta ADE

Hence by c.p.c.t., we can say that :                BC\ =\ DE

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