Video Transcript
Are any two equilateral triangles
congruent?
Let’s begin this question by
recalling that congruent triangles are a type of congruent polygon. So all pairs of corresponding
angles are congruent, and all pairs of corresponding sides are congruent. And we know that equilateral
triangles are triangles that have three congruent sides. So we could, for example, have an
equilateral triangle which has every length as five centimeters. As the sides are congruent, then we
also know that all the angles in an equilateral triangle have measures of 60 degrees
each.
Now let’s imagine that we draw
another equilateral triangle that has sides of five centimeters each. We know that all the corresponding
angles will be congruent because they are all 60 degrees in measure. And all the corresponding pairs of
sides are congruent because they are all five centimeters. So these two equilateral triangles
are congruent. But what happens if we draw a
different equilateral triangle, something like this?
As it is an equilateral triangle,
all the angles will have a measure of 60 degrees. However, the sides are a little bit
longer, at seven centimeters each. Are these triangles congruent? Well, we do have that all the
corresponding angles are congruent because they are still 60 degrees in measure. However, all the corresponding
pairs of sides are not congruent, because we know that one equilateral triangle has
sides of five centimeters and the other one has sides of seven centimeters. So, when we consider the question
“Are any two equilateral triangles congruent?,” the answer is no. The two equilateral triangles drawn
below are not congruent.
However, it is easy to be confused
by some of the mathematical words that we use, because there is a word we can use to
describe the relationship between any two equilateral triangles. And it is the word “similar.” Similar polygons have corresponding
angles congruent. But rather than having
corresponding sides congruent, as we do in congruent polygons, similar polygons have
corresponding sides in proportion.
So the two equilateral triangles
drawn here are similar. And any two equilateral triangles
can be described as similar. But they are not always congruent,
which is why the answer to the question must be no.
