Similar Triangles

An architect designs an office building and builds a small-scale model for a client. The sides of the building have triangular glass panels.

In the model, these triangles are smaller but have the same shape. In geometry, triangles with the same shape, regardless of size, are called similar triangles.

In similar triangles, the corresponding angles in the two triangles are equal in measure. Their corresponding sides are proportional, meaning all side lengths change by the same scale factor.

For example, if every model side is one-tenth the length of the corresponding actual side, the triangles are similar. We can confirm this using the triangle similarity criteria.

The first is Angle-Angle. Here, two corresponding angles in one triangle match two corresponding angles in another triangle.

The second is Side-Side-Side. Here, all three pairs of corresponding sides in the two triangles are proportional.

The third is Side-Angle-Side. Here, two pairs of corresponding sides in the two triangles are proportional, and the included angles between these sides are equal.

Using these criteria, architects can check that each model panel accurately matches its actual panel.