Triangle tricks
Triangles are tricky shapes. You can do some surprising things with
them.
Let’s make a triangle that you can do some tricks with. You’ll need a
piece of paper about the size of this book, and a scissors.
First, fold the paper in half by bringing the top edge down to the
bottom edge. Now, with the folded edge at the top, take the upper
left-hand corner and fold it slantwise toward you, so that the corner is
even with the bottom edge of the paper. Crease the fold. Now, unfold the
paper. With the scissors, cut along the fold marks that form the large
triangle.
This one triangle is really two different kinds of triangles. You can
see the two triangles more easily if you move the paper triangle around.
Put the longest side at the bottom and you’ll see that the two “legs”
are the same length. So, you have the kind of triangle called an
isosceles triangle. Now move the triangle around until one of the “legs”
is at the bottom. You’ll see that one of the angles at the bottom is a
right angle. So, you also have a right triangle.
Cut your triangle in half, along the fold line. Now you have two
triangles, each one shaped exactly the same as the big one you had
before.
Place the two triangles side by side, with the long side at the bottom.
Turn one triangle around until the long side is at the top. Now slide
the two triangles together.
The two triangles now form a shape called a parallelogram (par uh
[lehl]{.smallcaps} uh gram). Look at this shape carefully. You’ll see
that the sides that are across from each other are the same length.
These sides are also parallel—that is, they are the same distance
apart at all points. (You can measure them and see.)
Next, move one triangle around until the right angle is at the lower
left. Move the other triangle until the right angle is at the lower
right.
Now, turn one triangle so that its long side fits against the long side
of the other. What shape do you have now?
A square, of course! To be a square, a shape must have four right angles
and four sides that are all the same length.
Fold each of the two triangles in half and cut along the fold lines.
With a little practice, you will find that you can fit these four
triangles together to make many shapes and designs.
square
Then, cut each of the four triangles in half again, so that you have
eight triangles. You’ll find that you can now make quite different
shapes and designs.
Here are a few of the ways in which you can put triangles together to
make interesting shapes and designs.
