Question
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) \( \angle A B C \cong \angle E D F \)
Ask by Conner Vaughn. in China
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
所有选项都是正确的，没有错误的陈述。
Solution
在不等边三角形 \( A B C \) 与三角形 \( D E F \) 相似的情况下，以下哪个陈述是 \( f a l s e \)？
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) \( \angle A B C \cong \angle E D F \)
我们来分析每个选项：
1) 由于三角形相似，边的比率是相等的，因此 \( A B: B C=D E: E F \) 是正确的。
2) 由于三角形相似，边的比率是相等的，因此 \( A C: D F=B C: E F \) 也是正确的。
3) 由于三角形相似，角相等，因此 \( \angle A C B \cong \angle D F E \) 是正确的。
4) 由于三角形相似，角相等，因此 \( \angle A B C \cong \angle E D F \) 也是正确的。
综上所述，所有选项都是正确的，因此没有明显的错误陈述。请确认题目是否有误或提供更多信息。
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Extra Insights
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!
