Answer:
all equilateral triangle’s can be mapped onto each other using dilations.
Step-by-step explanation:
Because you can dilate or increase the size and scale the triangle about a certain point so if you do it correctly, this can be done with just a dilation.
Also an equilateral triangle is defined as a triangle where all the sides are congruent in length. This does not mean that all equilateral triangles are congruent (Do not get confused with D) to each other since size is the undefined variable so all equilateral triangles are proportional which means that they always have a ratio between them depending on the scale factor.
For example, let's say I have an equilateral triangle with a side length of 2, this means that all the sides must have a length of 2, but I can also have an equilateral triangle with a side length of 3, which means that all the sides will have that length for that triangle.
2 ≠ 3, but there is always a conversion factor between the side lengths. In this case a scale factor of 3/2 from the triangle with a side length of 2 to the one with a side length of 3. And a scale factor of 2/3 going from the triangle with a side length of 3 to the triangle with a side length of 2. Because all the sides are congruent, the angles must all be 60° degrees because individual side proportions defined by trigonometry are based on angles and sides. Thus, the angles are also affected due to the change in ratio.
