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In DeltaABC , if L and M are the points ...

In `DeltaABC` , if L and M are the points on AB and AC, respectively such that `LM || BC`. Prove that `ar (DeltaLOB) = ar (DeltaMOC)`.

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To prove that \( \text{ar}(\Delta LOB) = \text{ar}(\Delta MOC) \) given that \( LM \parallel BC \) in triangle \( ABC \), we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Triangles**: We have triangle \( ABC \) and points \( L \) and \( M \) on sides \( AB \) and \( AC \) respectively, such that \( LM \parallel BC \). 2. **Use the Area Theorem**: According to the theorem, triangles that are on the same base and between the same parallel lines have equal areas. Here, we will consider triangles \( LBC \) and \( MBC \). ...
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