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The question asks for the missing step in the proof, where **AB** is proven parallel to **DF**.

From the given problem:

- We know that point **B** is the midpoint of segment **EF**, and point **A** is the midpoint of segment **ED**.
- Step 2 calculates the midpoints of **DE** and **EF** using the midpoint formula.
- Step 3 calculates the slopes of line segments **AB** and **DF**.
- Step 4 states that the slopes of **AB** and **DF** are equal using the **Substitution Property of Equality**.

The final step (Step 5) concludes that **AB** is parallel to **DF**.

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To justify this conclusion, we need to define **parallel lines** mathematically. The **definition of parallel lines** states that two lines are parallel if and only if their slopes are equal.

Thus, the missing step in the proof is:

### **B. Definition of parallel lines**

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Would you like me to explain any part of this in further detail? Here are 5 related questions:

1. What is the definition of the slope of a line?
2. How do you calculate the midpoint of a segment?
3. What does the Substitution Property of Equality mean in geometry?
4. What is the relationship between equal slopes and parallel lines?
5. How can you prove two segments are congruent using midpoints?

**Tip:** When solving geometry proofs, carefully match each statement with the appropriate definition, property, or theorem!

Erica is given the diagram below and asked to prove that AB is parallel to DF. What would be the missing step of the proof?

Learn how to prove that two lines are parallel using midpoints and slopes in coordinate geometry. In this problem, the midpoint and slope formulas are applied to show that AB is parallel to DF. Suitable for Grade 9-10 geometry students.

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