Answered

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Given: D is the midpoint of AB; E is the midpoint of AC. Prove: DE ∥ BC On a coordinate plane, triangle A B C is shown. Line segment D E goes from side A B to side A C. Point A is at (2 b, 2c), point E is at (a + b, c), point C is at (2 a, 0), point B is at (0, 0), and point D is at (b, c). 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 = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction = StartFraction c minus c Over a + b minus b EndFraction = = slope of BC = Therefore, because , DE ∥ BC.

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