Let us first learn how to construct a triangle if we are given the lengths of the sides. Have your ruler and compasses out and follow along with the applet, constructing your own triangle. Use for example lengths 3 inches for AB, 4 inches for AC and 2 inches for BC.
If two of the sides of a triangle are equal we say that it is an isosceles triangle. Construct for yourself ten isosceles triangles ABC with sides AB and AC equal in length. Make a table of the measures of the angles like the one below. What do you observe?
| Length of AB | Length of AC | Length of BC | Measure of A | Measure of B | Measure of C |
| 1 inch | 1 inch | 1.5 inches | 40° | 70° | 70° |
If all three sides are equal then we say the triangle is an equilateral triangle. How large are the angles in an equilateral triangle?
Right Triangles
We shall be interested in triangles in which one of the angles is a right angle. We call them right triangles. In a right triangle we call the longest side (the one that is opposite the right angle) the hypotenuse. The other sides are called legs. Below is a picture of a right triangle. The vertices are labeled with capital letters A, B, and C. The lower case letters represent the lengths of the sides. Notice that the side a is opposite angle A and so on. The side AB is the hypotenuse.
