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

April 12, 2026Mathematics

ScanSolve AI Answer

April 12, 2026

Answer

$\triangle GDE \sim \triangle GBA$ by AAA similarity

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

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Use the property of similar triangles formed by parallel lines DE AB. Consider GDE and GBA.

Asked on April 12, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 12, 2026

Step 1: Use the property of similar triangles formed by parallel lines DE AB. Consider GDE and GBA. Since DE AB, we have: G is common to both triangles. GDE = GBA (corresponding angles, as DE AB and GB is a transversal). GED = GAB (corresponding angles, as DE AB and GA is a transversal). Therefore, GDE GBA by AAA similarity. From the similarity, the ratio of corresponding sides is equal: (GD)/(GB) = (GE)/(GA)