The question asks how Kylie can construct a second triangle $\triangle DEF$ such that it is similar to $\triangle ABC$. To ensure similarity between the triangles ($\triangle DEF \sim \triangle ABC$), their corresponding angles must be congruent, and the sides must be proportional.

Analysis of Each Option:

1. Duplicate $\overline{BC}$ as $\overline{EF}$: This does not ensure similarity because side lengths need to be proportional, not necessarily duplicated.

2. Construct $\overline{AB}$ proportional to $\overline{DE}$: This ensures the sides are proportional, which is a necessary condition for similarity.

3. Construct $\angle B$ congruent to $\angle E$: Congruent corresponding angles are a requirement for similarity, so this is correct.

4. Construct $\angle C$ congruent to $\angle F$: This is another necessary condition for similarity as it matches corresponding angles.

Correct Answers:

• Construct $\overline{AB}$ proportional to $\overline{DE}$
• Construct $\angle B$ congruent to $\angle E$
• Construct $\angle C$ congruent to $\angle F$

These steps will ensure the triangles are similar.

Would you like additional explanation or have further questions? Here are 5 related questions for further exploration:

1. What is the difference between congruence and similarity in triangles?
2. How do you construct a triangle given one angle and proportional side lengths?
3. Why is it necessary to match corresponding angles for triangle similarity?
4. What is the AA (Angle-Angle) similarity criterion?
5. How does the proportionality of sides ensure triangle similarity?

Tip: When working with similarity, focus on ensuring proportional side lengths and congruent corresponding angles.