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  • In Fig, AC = AE, AB = AD and ∠ BAD = ∠ EAC. Show that BC = DE.

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

    

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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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Devendra Khairwa

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