How Can We Make These Shapes Congruent? Symmetry!

I find symmetry to be an interesting subject to learn about, it may be simple, but I enjoy it. One type of symmetry is line symmetry, a figure has line symmetry if it divides a figure into two congruent halves. For those who may not know, congruent means the same thing as equal, but when doing geometry the word conguent is used instead. In class we practiced line symmetry with four regular polygons, a triangle, square, pentagon, and a hexagon. When I was first drawing the lines of symmetry in these shapes I thought that the triangle only had one line of symmetry and was a little surprised to find out there are three lines of symmetry. I realized that I failed to rotate my paper to see the other two lines of symmetry, but as soon as I did rotate the paper I understood why there were three lines sof symmetry in the regualr triangle.

Another symmetry that we learned about was rotational symmetry. A figure has rotational symmetry when it is rotated 0 degrees and 360 degrees the resulting figure coincides with the original. The number of times you get and identical figure when rotating the figure is called the order. For this we cut out a square, trappezoid, and a rhombus, then we were given a piece of paper and 3 brads (or paper fasteners if you don't know them as brads) to attach the shapes to the given paper so that you can still rotate them. This helped to show that a trapezoid does not have any rotational symmetry because when you rotate it there is no point in the rotation when it is symmetrical to the original position. The square had order 4 rotational symmetry, meaning that at 4 points of the rotation the figure is symmetrical to the original figure. The rhombus was order 2 in rotational symmetry, similarly to the square, this means that when rotating the rhombus there were two times in the rotation that the rhombus was symmetrical to the original figure.

https://www.mathsisfun.com/geometry/symmetry.html

The following two pictures are showing the activities that we did with the lesson.