1.(i) \small \Delta ABC and \small \Delta DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig.). If AD is extended to intersect BC at P, show that

 (i) \small \Delta ABD\cong \Delta ACD 

                                    

Answers (1)

Consider \Delta ABD  and   \Delta ACD ,

(i)  AD\ =\ AD             (Common)

(ii)   AB\ =\ AC            (Isosceles triangle)

(iii)   BD\ =\ CD          (Isosceles triangle)

Thus by SSS congruency we can conclude that : 

  \small \Delta ABD\cong \Delta ACD

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