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)

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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