Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side.

Given: ∆ABC

Prove: The midsegment between sides and is parallel to side .

Draw ∆ABC on the coordinate plane with point A at the origin (0, 0). Let point B have the ordered pair (x1, y1) and locate point C on the x-axis at (x2, 0). Point D is the midpoint of with coordinates at by the Distance between Two Points Postulate. Point E is the midpoint of with coordinates of by the Distance between Two Points Postulate.

Question

Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side.

Given: ∆ABC

Prove: The midsegment between sides  and  is parallel to side .

Draw ∆ABC on the coordinate plane with point A at the origin (0, 0). Let point B have the ordered pair (x1, y1) and locate point C on the x-axis at (x2, 0). Point D is the midpoint of  with coordinates at  by the Distance between Two Points Postulate. Point E is the midpoint of  with coordinates of  by the Distance between Two Points Postulate.