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 Midpoint Formula. Point E is the midpoint of with coordinates of by the Midpoint Formula. The slope of is found to be 0 through the application of the slope f

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 Midpoint Formula. Point E is the midpoint of  with coordinates of  by the Midpoint Formula. The slope of  is found to be 0 through the application of the slope f

anonymous · Answer

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 Parallel Postulate.

Which statement corrects the flaw in Gina's proof? 

 The coordinates of D and E were found using the slope formula. 

 Segments DE and AC are parallel by definition of parallel lines. 

 The coordinates of D and E were found using the Distance between Two Points Postulate 

 The slope of segments DE and AC is not 0.