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Two sides and the perimeter of one trian...

Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

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To determine whether the two triangles are similar based on the given conditions, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Triangles**: Let’s denote the first triangle as \( \triangle ABC \) and the second triangle as \( \triangle DEF \). 2. **Assign Sides**: Let the sides of triangle \( ABC \) be \( a \), \( b \), and \( c \). According to the problem, the corresponding sides of triangle \( DEF \) will be \( 3a \), \( 3b \), and \( f \) (where \( f \) is the third side of triangle \( DEF \)). ...
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