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Question
1/ \DeltaABC and \( \Delta \) DBC are two isosceles triangles on
the same base BC and verticeles triangles on same side of \( \mathrm { BC } \) (see Fig. 7.39 ). If \( \mathrm { AD } \) is extended to intersect \( \mathrm { BC } \) at \( \mathrm { P } \), show that (i) \( \quad \Delta A B D \cong \Delta A C D \) (ii) \( \Delta \mathrm { ABP } \cong \Delta \mathrm { ACP } \) (iii) APbisects \( \angle \) Aas well as \( \angle \mathrm { D } \) (iv) \( \mathrm { AP } \) is the perpendicular bisector of \( \mathrm { BC } \)
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