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.The slope of is found to be

Answer 1

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. The slope of is found to be 0 through the application of the slope formula: When the slope formula is applied to , its slope is also 0. Since the slope of and are identical, and are parallel by the definition of parallel lines.

Which statement corrects the flaw in Gina's proof?

The slope of segments DE and AC is not 0.

Segments DE and AC are parallel by construction.

The coordinates of D and E were found using the Midpoint Formula.

The coordinates of D and E were found using the slope formula.