# 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) $\small \Delta ABD\cong \Delta ACD$

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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