Learn these symbols and keep an eye out for them!Similar Triangles
Similar triangles have the same shape, but they are not necessarily the same size. Having the same shape
means that the angles of the triangles are identical and that the corresponding sides have the same ratio.
Look at the following two similar triangles:
These two triangles both have the same set of angles, but they aren’t the same size. Whenever this is true,
the sides of one triangle are proportional to those of the other. Notice that sides NO and ST are both
opposite the angle that is a°. These are called corresponding sides, because they correspond to the same
angle. So the lengths of NO and ST are proportional to each other. In order to figure out the lengths of the
other sides we set up a proportion: . Now fill in the information that you know:.
Cross-multiply and you find that x = 21. You could also figure out the length of y: . So,
, and y = 36. Whenever you have to deal with sides of similar triangles, just set up a proportion.Finally, there’s a special relationship between similar triangles and trigonometry. Side lengths in similar
triangles are proportional, and the trigonometric functions give the proportions of the sides of a triangle.
Therefore, if two triangles are similar, the corresponding trigonometric functions are equal! Let’s look at
how this might work in a problem.