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"1. \\( \\Delta \\mathrm { ABC } \\) and \\( \\Delta \\mathrm { DBC } \\) are two isosceles triangles on\nthe same base \\( \\mathrm { BC } \\) and vertices \\( \\mathrm { A } \\) and \\( \\mathrm { D } \\) are on the\nsame side of \\( \\mathrm { BC } \\) (see Fig. 7.39 ). If \\( \\mathrm { AD } \\) is extended\nto intersect \\( \\mathrm { BC } \\) at \\( \\mathrm { P } \\), show that\n(1) \\( \\Delta \\mathrm { ABD } \\equiv \\Delta \\mathrm { ACD } \\)\n(ii) \\( \\Delta \\mathrm { ABP } \\equiv \\Delta \\mathrm { ACP } \\)\n(iii) AP bisects \\( \\angle \\mathrm { A } \\) as well as \\( \\angle \\mathrm { D } \\).\n(iii) AP bisects \\( \\angle \\mathrm { A } \\) as well as \\( \\angle \\mathrm { D } \\).\n(iv) AP is the perpendicular bisector of BC in which \\( \\mathrm { AB } = \\) AC. Show the"
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Q1
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