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.