5.  ABC and DBC are two isosceles triangles on the same base BC (see Fig.). Show that \small \angle ABD\ \cong \ \angle ACD .

                             

Answers (1)

Consider \Delta ABD  and   \Delta ACD,

(i)   AD\ =\ AD    (Common in both the triangles)

(ii)   AB\ =\ AC         (Sides of isosceles triangle)

(iii)   BD\ =\ CD       (Sides of isosceles triangle)

Thus by SSS congruency, we can conclude that :

 \small \angle ABD\ \cong \ \angle ACD

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