Question Video: Determining If Any Two Equilateral Triangles Are Congruent | Nagwa Question Video: Determining If Any Two Equilateral Triangles Are Congruent | Nagwa

# Question Video: Determining If Any Two Equilateral Triangles Are Congruent Mathematics • First Year of Preparatory School

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Are any two equilateral triangles congruent?

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### 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.

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