Triangle Similarity 4B9168

1. State the problem: We need to prove that $\triangle YOG$ is similar to $\triangle FOX$ given that $FX \parallel YG$. 2. Given: $FX \parallel YG$ (Given) 3. Use the property of parallel lines: Since $FX \parallel YG$, the corresponding angles formed by the transversal $OY$ are congruent. 4. Identify congruent angles: $\angle FOX \cong \angle YOG$ (Corresponding Angles Postulate) 5. Reflexive property: $\angle O$ is common to both triangles, so $\angle O \cong \angle O$ (Reflexive Property of Congruence) 6. Apply AA similarity criterion: Since two pairs of corresponding angles are congruent, $\triangle YOG \sim \triangle FOX$ (AA similarity criterion). Final proof table: Statements: 1) $FX \parallel YG$ 2) $\angle FOX \cong \angle YOG$ 3) $\angle O \cong \angle O$ 4) $\triangle YOG \sim \triangle FOX$ Reasons: 1) Given 2) Corresponding Angles Postulate 3) Reflexive Property of Congruence 4) AA similarity criterion