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triangleABC and triangleDBC are two isos...

`triangleABC` and `triangleDBC` are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that:
(i) `triangleABD ~= triangleACD`
(ii) `triangleABP ~= triangleACP`
(iii) AP bisects `angleA` as well as `angleD`
(iv) AP is the perpendicular bisector of BC.

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