Given triangle $ABC$ with angles $A$, $B$, and $C$, which of the following triangles could ∤ be similar to triangle $ABC$?

• A. A triangle with angles $A$, $B$, and $C$
• B. A triangle with angles $60$°, $60$°, and $60$°
• C. A triangle with angles $B$, $C$, and $A$
• D. A triangle with angles $C$, $A$, and $B$

Answer: (B)

Verified step by step guidance

1. Recall that two triangles are similar if and only if their corresponding angles are equal. This means the angles of one triangle must match the angles of the other triangle in measure, regardless of the order of the vertices.
2. Identify the angles of the original triangle \( \triangle ABC \) as \( A, B, \) and \( C \). Any triangle with angles \( A, B, \) and \( C \) in any order will be similar to \( \triangle ABC \) because the angle measures are the same.
3. Examine the given options: triangles with angles \( A, B, C \), \( B, C, A \), and \( C, A, B \) all have the same angle measures as \( \triangle ABC \), just in different orders, so they are similar to \( \triangle ABC \).
4. Consider the triangle with angles \( 60^\circ, 60^\circ, 60^\circ \). Since all angles are equal to 60 degrees, this triangle is equilateral and its angles do not necessarily match the angles \( A, B, \) and \( C \) of \( \triangle ABC \) unless \( A = B = C = 60^\circ \).
5. Therefore, the triangle with angles \( 60^\circ, 60^\circ, 60^\circ \) could NOT be similar to \( \triangle ABC \) unless \( \triangle ABC \) is also equilateral. This is because similarity requires matching angle measures.