You can draw your cat on paper. You’ll need a wide assortment of triangles. You’ll need a large wide triangle for the body and a smaller triangle for the head. You’ll need narrow triangles for the whiskers and tail. You’ll need small triangles for the eyes and even smaller triangles for the pupils of the eyes.

Here’s what you’ll need:

A pencil, a ruler, a protractor

Scissors and paste, if you wish

Here’s how to make your cat from triangles:

1. Begin with a body for your cat. With the ruler, draw a straight line on the paper. That’s the base line for a triangle
2. Use the protractor to measure angles for different types of triangles. (If you need help in using the protractor, we will show you how.)
3. If you want a cat of many colors, draw triangles on construction paper of different colors. Cut the triangles out, and paste them onto a large sheet of paper.

You probably used some very special triangles to design your cat. Now find out the secrets they hold.

Here’s how to use your cat to discover triangle secrets:

1. Each of your cat triangles has three sides and three angles, but that may not be all they have in common.
   You can use a protractor to measure the three angles of each of your triangles. Add the number of degrees for all three angles of your biggest triangle. Add the three angles of your smaller triangles. Try a medium triangle.
   Have you discovered something else that is the same for every triangle? Look for the answer at * below.
2. If you know the number of degrees for two angles in a triangle, you can figure out how many degrees are in the third angle.
   Add the two angles. Then subtract the sum from 180. That’s the number of degrees in the third angle.
3. Does one of your triangles have two sides of equal length? If so, you can discover that two or perhaps all three of the angles are the same. Use a protractor to find out.
   This special triangle, with two equal sides and two or three equal angles is an isosceles triangle.
4. Does one of your triangles have two sides of equal length plus a 60-degree angle?
   If so, you have created a very special triangle. You’ll find that each of the three angles measures 60 degrees, and all three sides are of equal length. All the sides are equal, and so are all the angles.

* If you measure three angles of any triangle and then add them up, you’ll find the sum is always 180 degrees. You can try it here:

(click image to print)

The ideas for this unit come from M. Kenda and P. Williams (1995). Math Wizardry for Kids, Happauge, NY: Barron’s Educational Series, Inc., pp. 14-16.