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D and E are points on sides AB and AC r...

`D` and `E` are points on sides `AB` and `AC` respectively of `Delta A B C` such that `a r\ (D B C)\ =\ a r\ (E B C)`. Prove that `D E||B C`.

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To solve the problem, we need to prove that line segment DE is parallel to line segment BC given that the areas of triangles DBC and EBC are equal. ### Step-by-Step Solution: 1. **Identify the Given Information**: - We have triangle ABC. - Points D and E are on sides AB and AC, respectively. - The areas of triangles DBC and EBC are equal: \( \text{Area}(DBC) = \text{Area}(EBC) \). ...
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