## Understanding Point Symmetry

In the previous post, we have learned about line symmetry. In this post, we are going to learn about point symmetry, another type of symmetry.

If a figure is rotated 180 degrees about a point and it coincides with its original position, then it is said that the figure has point symmetry. The point of rotation is called the point of symmetry.

The figure below shows the point symmetric polygon ABCDEF rotated clockwise about P, its point of symmetry. The polygon outlined by the dashed line segments shows its original position.  » Read more

## 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

## Derivation of the Area of a Rhombus

A rhombus is a parallelogram whose sides are congruent. The diagonals of rhombus are perpendicular to each other. They also bisect each other. In this post, we are going to find the general formula for finding the area of a rhombus using these properties. We are going to learn two methods.

Method 1

Consider the rhombus below. We can divide it into two congruent triangles using diagonal $d_1$. Since the diagonals of a rhombus are perpendicular to each other, we can use $d_1$ as base and one half of $d_2$ as the height of the upper triangle (Why?). If we let $A_T$ be the area of the upper triangle, then, calculating its area, we have  » Read more

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