In a scalene triangle \( A B C \) is similar to triangle \( D E F \). Which statement is \( f a l s e \) ? 1) \( A B: B C=D E: E F \) 2) \( A C: D F=B C: E F \) 3) \( \angle A C B \cong \angle D F E \) 4) \( \angle A B C \cong \angle E D F \)
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In similar triangles, corresponding angles are congruent, and the lengths of corresponding sides are in proportion. However, in this case, the false statement would be 2) \( A C: D F=B C: E F \). This is incorrect because it does not maintain the ratio of corresponding sides consistently across the triangles. For statement 1, 3, and 4, the relationships established follow the properties of similar triangles, where ratios of sides must match and angles must be congruent. Always remember to match the triangle's vertices correctly when establishing the relationships!