Question

consider the triangle. triangle with three 60° angles which statement is true about the lengths of the sides? the sum of the lengths of two sides is equal to the length of the third side. the three sides have the same length. two sides have the same length, which is less than the length of the third side. each side has a different length.

Explanation:

Step1: Identify the triangle type

The triangle has three angles of \(60^\circ\). By the angle - sum property of a triangle (sum of interior angles of a triangle is \(180^\circ\)), and since all three angles are equal, this is an equilateral triangle.

Step2: Recall properties of equilateral triangles

In an equilateral triangle, all three sides are of equal length. Now let's analyze each option:

• Option 1: "The sum of the lengths of two sides is equal to the length of the third side." This is false. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side (triangle inequality theorem), and for an equilateral triangle with side length \(a\), \(a + a=2a> a\).
• Option 2: "The three sides have the same length." This is true because it is an equilateral triangle.
• Option 3: "Two sides have the same length, which is less than the length of the third side." This is false. In an equilateral triangle, all sides are equal.
• Option 4: "Each side has a different length." This is false. In an equilateral triangle, all sides are equal.

Answer:

The three sides have the same length.