1.(ii)  ∆ 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

 (ii) \small \Delta ABP \cong \Delta ACP

              

Answers (1)
D Devendra Khairwa

Consider \Delta ABP  and   \Delta ACP,

(i)  AP  is common side in both the triangles.

(ii)  \angle PAB\ =\ \angle PAC                       (This is obtained from the c.p.c.t. as proved in the previous part.)

(iii)   AB\ =\ AC                                    (Isosceles triangles)

Thus by SAS axiom, we can conclude that :

    \small \Delta ABP \cong \Delta ACP

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