Question

decide whether each statement is true or false.
an equilateral triangle has 3 acute angles. \t\ttrue \t\tfalse
an isosceles triangle has 2 equal side lengths. \t\ttrue \t\tfalse

Explanation:

Step1: Analyze the first statement

Recall the properties of an equilateral triangle: all sides are equal, and all angles are equal. The sum of angles in a triangle is \(180^\circ\), so each angle in an equilateral triangle is \(\frac{180^\circ}{3} = 60^\circ\). An acute angle is an angle less than \(90^\circ\), and \(60^\circ<90^\circ\), so each of the three angles is acute. Thus, the statement "An equilateral triangle has 3 acute angles" is true.

Step2: Analyze the second statement

Recall the definition of an isosceles triangle: a triangle with at least two equal side lengths (by some definitions, exactly two, but the common understanding includes at least two). So, an isosceles triangle has 2 (or 3, in the case of equilateral which is a special isosceles) equal side lengths. Thus, the statement "An isosceles triangle has 2 equal side lengths" is true.

Answer:

For "An equilateral triangle has 3 acute angles": True (select the True circle).
For "An isosceles triangle has 2 equal side lengths": True (select the True circle).