1. Since the triangles are different sizes, we will start by dilating ΔABC to a smaller size. The smaller size needs to match the side lengths of ΔDEF, so we match AB with DE by setting the scale factor to be . The new dilated triangle will be ΔA'B'C'.
2. After the dilation, we know that ΔA'B'C'∼ΔABC because a dilation is a similarity transformation.
3. After the dilation, ∠A ∠A' and ∠B ∠B' since dilations preserve angle measure.
4. After the dilation, A'B' = k•AB = DE, which gives us .
5. We are given that ∠A ∠D and ∠B ∠E, and from step 3 that ∠A ∠A' and ∠B ∠B'. Using the transitive property, we get ∠A' ∠D and ∠B' ∠E.
6. ΔA'B'C' ΔDEF by angle side angle (ASA) for congruent triangles.
7. Since ΔA'B'C' ΔDEF and ΔA'B'C' ∼ ΔABC, we have ΔDEF ∼ ΔABC. |