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  2. ∆ ABC and ∆ 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) ∆ ABD ≅ ∆ ACD
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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)
S Sanket Gandhi

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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