If the length of each side of a triangle is one-third of its perimeter, how many lines of symmetry does it have?
The first thing we can do is draw an example of this kind of triangle. We know that the length of each side of a triangle is one-third of its perimeter. We also know, to find the perimeter of a triangle, the distance all the way around, we have to add the lengths of every side. So we say side plus side plus side equals perimeter.
Our problem tells us that one-third plus one-third plus one-third equals the perimeter. Each side of our triangle is the same length. We can use a ruler to draw an example of a triangle where every side is the same length.
Let’s make a triangle where each side is four centimeters. Now that we’ve sketched our triangle, we can think about what lines of symmetry mean. Lines of symmetry are imaginary lines where you could fold the image and both halves would match exactly.
Here’s an example of a line of symmetry. If we folded our triangle on this yellow line, both halves would match perfectly. Here’s another one. You could fold the triangle at the second yellow line and still both halves would match. Here’s our third and final line of symmetry.
For every triangle that’s equilateral, for every triangle where every side is the same length, it will have three lines of symmetry.