Question

complete the similarity statement. an equilateral triangle is sometimes/always/never similar to a scalene triangle, because we can sometimes/always/never map one onto the other using only dilations and rigid transformations.

Explanation:

Step1: Recall triangle properties

An equilateral triangle has all sides equal and all angles equal to \(60^{\circ}\). A scalene triangle has all sides of different lengths and all angles of different measures.

Step2: Check similarity conditions

For two triangles to be similar, their corresponding angles must be equal. Since an equilateral triangle has all angles \(60^{\circ}\) and a scalene triangle has angles of different measures, we can never have an equilateral triangle similar to a scalene triangle. Also, if we want to map two similar triangles using dilations and rigid transformations, the angle - measure condition for similarity must be met. Since the angle measures of an equilateral and a scalene triangle can never be equal, we can never map an equilateral triangle onto a scalene triangle using only dilations and rigid transformations.

Answer:

An equilateral triangle is never similar to a scalene triangle, because we can never map one onto the other using only dilations and rigid transformations.