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Prove that GDE GBA using the given condition DE AB and explain the steps.

Mathematics

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Step 1: Use the property of similar triangles formed by parallel lines DE∥ABDE \parallel AB.
Consider △GDE\triangle GDE and △GBA\triangle GBA.
Since DE∥ABDE \parallel AB, we have:
∠G\angle G is common to both triangles.
∠GDE=∠GBA\angle GDE = \angle GBA (corresponding angles, as DE∥ABDE \parallel AB and GBGB is a transversal).
∠GED=∠GAB\angle GED = \angle GAB (corresponding angles, as DE∥ABDE \parallel AB and GAGA is a transversal).
Therefore, △GDE∼△GBA\triangle GDE \sim \triangle GBA by AAA similarity.
From the similarity, the ratio of corresponding sides is equal:

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