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Given: D is the midpoint of AB; E is the midpoint of AC. Prove: DE ∥ BC Complete the missing parts of the paragraph proof. Proof: To prove that DE and BC are parallel, we need to show that they have the same slope. slope of DE = = = slope of BC = Therefore, because , DE ∥ BC.

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Answer:

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the slopes are equal is right.

Step-by-step explanation:

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Parallel lines are those pair of lines which are never intersect to each other.

Both lines DE and BC are parallel  to each other.

Since, here a figure is attached .

In that figure, coordinate of D are (b, c) and coordinate of E are ( a+b , c )

and In line BC , coordinate of point b are (0, 0) and coordinate of point C are (2a, 0).

If two lines have same slope then those lines are parallel lines.

slope of line DE,  [tex]=\frac{c-c}{a}=0[/tex]

Slope of line BC ,  [tex]=\frac{0-0}{2a}=0[/tex]  

Since, both lines have same slope. Therefore, line DE and BC are parallel.

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