Question

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a triangle, △ abc, has angle measures of 60°, 60°, and 60° and three congruent (equal) sides. how would this triangle be classified?
○ equilateral obtuse
○ equilateral acute
○ isosceles acute
○ scalene acute

Explanation:

1. First, recall the definitions:

• An equilateral triangle has three congruent (equal) sides and three congruent angles (each \(60^\circ\)).
• An acute triangle has all angles less than \(90^\circ\) (since \(60^\circ<90^\circ\), all angles here are acute).
• An obtuse triangle has one angle greater than \(90^\circ\) (not the case here as all angles are \(60^\circ\)).
• An isosceles triangle has at least two congruent sides (this triangle has three, so it's equilateral, a special case of isosceles, but equilateral is more precise here).
• A scalene triangle has no congruent sides (this triangle has three congruent sides, so not scalene).

1. Analyze each option:

• "Equilateral obtuse": Obtuse triangles have an angle \(>90^\circ\), but this triangle's angles are \(60^\circ\), so eliminate.
• "Equilateral acute": It has three equal sides (equilateral) and all angles \(60^\circ\) (acute, since \(60^\circ < 90^\circ\)), so this fits.
• "Isosceles acute": While it is acute, it's more accurately equilateral (since all three sides are congruent, not just two), so "equilateral" is a better classification.
• "Scalene acute": Scalene triangles have no equal sides, but this triangle has three equal sides, so eliminate.

Answer:

B. Equilateral acute (assuming the options are labeled A, B, C, D with "Equilateral acute" as one of them; if the original options' numbering is different, adjust the label, but the text is "Equilateral acute")