Question

Draw two equilateral triangles that are not congruent.

Measure the side lengths and angles of your triangles. Are the two triangles similar?
Do you think two equilateral triangles will be similar always, sometimes, or never? Explain your reasoning.

Answer 1

Equilateral triangles that are not congruent can be created by scaling up or down a base equilateral triangle. Two equilateral triangles will always be similar because they have the same shape.

Step-by-step explanation:

An equilateral triangle is a triangle in which all three sides are equal in length and all three angles are equal to 60 degrees. To draw two equilateral triangles that are not congruent, we can start with a base equilateral triangle and create a second equilateral triangle by scaling it up or down.

For example, let's say the side length of the first equilateral triangle is 4 units. To create the second equilateral triangle, we can double the side length to 8 units. Now we have two equilateral triangles with side lengths of 4 units and 8 units, respectively.

Although the two triangles are not congruent, they are similar because they have the same shape but different sizes. The ratio of corresponding side lengths is the same for both triangles, which is 2:1 in this case. Therefore, two equilateral triangles will always be similar because they have the same shape.