SAS (Side-Angle-Side) Similarity

If two pairs of corresponding sides are proportional, and one pair of corresponding angles in two triangles are equal, then the two triangles are similar. However, that angle has to be the one between the two sides.

For example, in $\triangle ABC$ and $\triangle DEF$, we are given $\angle A = \angle D$. We then want to confirm $AB,\,AC\,,DE\,,DF$ are proportional. To check this, you can do one of the following two: $\\$

1. $\frac{AB}{AC}=\frac{DE}{DF}$ $\\$
2. $\frac{AB}{DE}=\frac{AC}{DF}$ $\\$

Once you confirm they are proportional, you can conclude $\triangle ABC \sim \triangle DEF$ $\\$ note: the two methods are slightly different, but you will notice they are mathematically equivalent.

Similarly, if you know $AB,\,AC\,,DE\,,DF$ are proportional, you want to confirm that $\angle A = \angle D$

Hi, let's do some problems on SAS similarity! On this worksheet please try problems 1, 3, 6, and 10-18. Have fun!