# 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) $\small \Delta ABP \cong \Delta ACP$

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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