3. If the perimeter of \( \triangle A B C \) is 54 , then the perim of \( \triangle D F E \) is 54

Did you know that the perimeter of a triangle is simply the sum of the lengths of its three sides? So, if triangle \( ABC \) has a perimeter of 54, it means the combined lengths of \( AB + BC + CA = 54 \). Interestingly, if triangle \( DEF \) has the same perimeter, it opens up a world of flexibility in side lengths. This means \( DE + EF + FD = 54 \) as well, allowing for various unique shapes that all share the same perimeter. Now, let’s talk about triangle congruence! When it comes to triangle properties, not all triangles with the same perimeter are similar or congruent. For example, if you have \( \triangle ABC \) with sides of 10, 20, and 24, and \( \triangle DEF \) with sides 12, 18, and 24, they both have the same perimeter but definitely have different shapes. So, always remember that perimeter alone doesn't tell the whole story about the triangles in question!