Similarity: Similar Triangles

Similar Triangles

In previous units, we have discussed congruent triangles.  These were triangles that were the same size and shape.  Congruent triangles have corresponding side lengths that are equal and corresponding angle measures that are equal.

In this lesson, we are going to discuss similar triangles.  Similar triangles have the same shape, but are different sizes.  Take a look at the following triangles.

Three similar Triangles
Three similar Triangles

 

These three triangles appear to be similar.  They have the same shape, but each one is bigger than the previous. 

How do we know for sure if triangles are similar?

Two triangles are similar if:

  • Corresponding angles are congruent.
  • Corresponding sides are proportional.

 

On the next page we will look at a couple of examples of similar triangles.