C. Symmetry
1. Fold Symmetry
you understand about folding symmetry, let's do the following experiment. Take a rectangular piece of paper. Name the vertices with the letters A, B, C, and D.
D C
A B
After that, fold the paper so that point A coincides with point B, and point D coincides with point C.
2. Axis of Symmetry
Take a look at the rectangle below! If rectangle ABCD is folded on line l, then point A will coincide with point B, and point D coincides with point C. So that line l, is called the axis of symmetry of rectangle ABCD. Likewise, line k is the axis of symmetry of rectangle ABCD. So, rectangle ABCD has two axes of symmetry.
D C
K
A B
3. Create a Symmetrical Shape
The following are the steps to create a symmetrical flat wake. Now let's study it well.
a. Try to have paper, scissors, and a ruler handy!
b. Fold the paper!
c. Make an arbitrary image on the paper that you folded earlier with the folded paper as one side!
d. Cut out the image that you have made (don't cut the side on the fold)!
e. Open up the image you cut out on the fold!
f. Once opened, you will get a symmetrical shape.
g. The line where you fold is the axis of symmetry of the shape.
4. Mirroring
Every morning before going to school, of course you look in the mirror first. You can see your reflection in the mirror exactly like you.
Let's learn the following steps.
- Try providing a flat mirror!
- Take a piece of paper!
- Then draw an arbitrary rectangle on the paper!
- Put a flat mirror on one side of the rectangle perpendicular to the paper!
- Now watch the shadows cast!
PICTURE AGAIN
The image above shows that the shadow shape is the same as the original shape. Thus, the properties of mirroring are:
a. line length does not change,
b. the shape of the shadow is the same as the original shape,
c. the shadow shape is symmetrical to the original shape.
5. Drawing Reflections
To understand how to draw a mirror, let's pay attention to the following example
1. Points A and D lie on the line k, so the shadows of points A and D do not change their location.
2. Determine the shadow B.
Draw a perpendicular line from point B to line k and extend the line! The image of point B, namely B', is to the right of line k and is the same distance from B to line k (k line is the middle of BB').
3. In the same way, determine the image of point C, namely C'!
4. Connect the points A', B', C', and D'!
5. The shape A'B'C'D' is the result of reflecting ABCD on the k line.