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 sides are in proportion and corresponding angles are congruent. However, the false statement among the options given is statement 2) \( A C: D F=B C: E F \). This statement mistakenly claims a proportional relationship between non-corresponding sides. For similar triangles, it's essential to only compare corresponding sides, which indeed are \( A B \) to \( D E \), \( B C \) to \( E F \), and \( A C \) to \( D F \). To remember, two triangles are similar if all their corresponding angles are equal and their corresponding sides are in proportion. So, when checking similar triangles, always align the correct angles and sides to avoid tripping over false statements. If you remember that, you'll avoid common pitfalls and mathematical misinterpretations in the future!