## Elementary Geometry for College Students (6th Edition)

$\triangle DGH$ ~ $\triangle DEF$ because of the Side-Side-Side Similarity Theorem
Side-Side-Side Similarity Theorem: If the lengths of corresponding sides of two triangles have the same ratio, then the triangles are similar. Since the lengths of the three sides of these triangles have the same ratio (in this case, the ratio is $\frac{1}{3}$), $\triangle DGH$ ~ $\triangle DEF$ $\triangle DGH$ ~ $\triangle DEF$ because of the Side-Side-Side Similarity Theorem