Understanding Line Symmetry

Many people believe that symmetry is beauty. Nature is full of symmetric objects. There are many man-made structures that are also symmetric. In this post, we are going to discuss some of the basic mathematical properties of symmetric objects. We will limit our discussion to line symmetric objects.

Line Symmetry

A figure is line symmetrical when it can be folded along a straight line such that the folded shapes fit exactly on top of each other. The fold line is called the line of symmetry.

When a symmetric figure is folded along its line of symmetry, the parts that are on top of each other are called the corresponding parts. In the polygon below with line of symmetry AB, points C and D are corresponding points, segments GB and HB are corresponding sides, and angle G and angle H are corresponding angles. Since the folded shapes fit exactly on top of each other, the corresponding angles are congruent and their corresponding sides are also congruent.  » Read more

The Search for Symmetric Words

The word MATH has a vertical line of symmetry. The parts of the letters on the left of the vertical line are reflected on the right. On the other hand, the word DECK has a horizontal line of symmetry.  The parts of the letters below horizontal line are reflected above.


The word OHIO is both horizontally and vertically symmetric.

Challenge: Find as many words as you can that are horizontally symmetric, vertically symmetric, and both. What are the longest symmetric words of each kind?