In triangles A B C and D E F, ∠ B = ∠ E, ∠ F = ∠ C, and A B = 3 D E. Then, the two triangles are:

Answered on : 2024-01-23

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Based on the given information:

1. ∠B = ∠E (Angles are equal)

2. ∠F = ∠C (Angles are equal)

3. AB = 3DE (Side AB is three times the length of side DE)

These conditions indicate that the two triangles are similar by the Angle-Angle-Side (AAS) similarity criterion. When two triangles have corresponding angles equal and the sides proportional, they are similar. In this case, ∆ABC is similar to ∆DEF, and you can denote this similarity as ∆ABC ~ ∆DEF.

This means that the corresponding angles of the two triangles are equal, and the sides are in proportion, which establishes the similarity between them.

References: None (Geometric similarity criterion)