Where to Look From - Mirror Halves and Symmetry

Different Views of Objects: Objects look different depending on where you look at them from. For example, a staircase looks like a series of rectangles from the side, but from the front, it looks like a single rectangular block. A pressure cooker looks like a cylinder with a handle from the side, but from the top, it looks like a circle with a small dot (the weight) and a handle sticking out.

Mirror Halves: A shape has mirror halves if it can be divided into two parts that are exactly the same. Imagine placing a small mirror on a dotted line; if the reflection in the mirror matches the hidden part of the picture, then the two parts are mirror halves. For example, if you place a mirror in the middle of a butterfly, the reflection will show a complete butterfly.

Line of Symmetry: The imaginary line that divides a shape into two identical mirror halves is called the line of symmetry. It is usually shown as a dotted line. If you fold a paper along this line, both halves will overlap perfectly. For instance, the letter $A$ has a vertical line of symmetry running down its center.

Vertical and Horizontal Symmetry: Some objects can be split top-to-bottom, which is called vertical symmetry (like the letter $M$ or $W$). Others can be split left-to-right, which is called horizontal symmetry (like the letter $E$ or $B$). Some shapes, like a circle or the letter $H$, have both vertical and horizontal symmetry.

Non-Symmetric Shapes: Not every object can be divided into mirror halves. If you try to draw a dotted line through a teapot or the letter $G$, you will find that the two sides do not look the same. These are called non-symmetric or asymmetrical objects.

Completing Symmetrical Pictures: You can use the idea of symmetry to complete half-drawn pictures. If you are given the left half of a square on a grid, you can draw the right half by mirroring the distance of each point from the central line. If a point is $3$ units to the left, its mirror point must be $3$ units to the right.

Symmetry in Letters and Numbers: Many letters in the alphabet are symmetrical. The letter $O$ has many lines of symmetry, while the letter $X$ has two. In numbers, $8$ and $0$ are usually symmetrical, but numbers like $4$, $5$, and $7$ are not.