## Geometry: Common Core (15th Edition)

The scale factor is the same for each set of corresponding sides; therefore, $\triangle YAM$ ~ $\triangle DEC$.
Similar polygons have congruent angles and proportional sides. If these two triangles are similar, we would expect the sides to be similar. We are given definite values for corresponding sides of the two triangles, so let us find the scale factor for the two triangles: $\frac{YM}{DC} = \frac{10}{5}$ Divide both the numerator and denominator by their greatest common factor, $5$, to simplify: $\frac{YM}{DC} = \frac{2}{1}$ So now we can compare this scale factor to the ratios of the other sets of corresponding sides: $\frac{AY}{ED} = \frac{8}{4}$ Divide both the numerator and denominator by their greatest common factor, $4$, to simplify: $\frac{AY}{ED} = \frac{2}{1}$ So far, the scale factor holds up for this set of corresponding sides. Let's check the last set: $\frac{AM}{EC} = \frac{6}{3}$ Divide both the numerator and denominator by their greatest common factor, $3$, to simplify: $\frac{AM}{EC} = \frac{2}{1}$ The scale factor is the same for each set of corresponding sides; therefore, $\triangle YAM$ ~ $\triangle DEC$.