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 Beauty of Mirrors and Symmetry

Symmetry is considered by many as a reflection of beauty and perfection. A symmetric object is an object where we can place a line such that the images on both sides of the line mirror each other.

line of symmetry

The geometric shapes in the first figure are symmetric. As shown, we can draw a line — in fact more than one line — to show symmetry. The equilateral triangle has three lines of symmetry, the square has four, and the circle has infinitely many. » Read more

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