Hands-on math!

Similar Triangles

Two triangles are similar if they have the same angles. Their sides don't have to be the same length. The ratio of their corresponding sides is called the scale factor. So, the two triangles here are similar because they have the same angles. The sides of the bigger one are twice the length of the sides of the little one, so their scale factor is 2.

This is sorta like congruent triangles, except congruent triangles have to be the same size. Just like with congruent figures, they can be turned in any relationship to each other, even mirror images.

The comparison below shows the relationship between congruent and similar triangles.
Notice that if you cut a triangle parallel to any one side, the two triangles you make will be similar:

In this example, if sides DE and BC are parallel, triangles ADE and ABC are similar.

Note: Other shapes can be similar too,
like rectangles, circles and combined shapes, like a triangle with a rectangle.