HELP!!!! ITS A LONG 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 AB and BC is parallel to side AC . 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). Label point D as the midpoint of with coordinates using midpoint formula

Question

HELP!!!! ITS A LONG 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 AB and BC is parallel to side AC . 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). Label point D as the midpoint of  with coordinates using midpoint formula

anonymous · Answer

Label point E so it is the midpoint of BC with an ordered pair by the Midpoint Formula. The slope of  DE is found to be 0 through the application of the slope formula. When the slope formula is applied to AC  its slope is also 0. Since the slope of DE  and AC are identical, they  are are parallel by the definition of parallel lines.

anonymous · Answer

What is the flaw in Gina’s proof?

 Points D and E must be constructed, not simply labeled, as midpoints.

 Segments DE and AC are parallel by construction.

 The slope of segments DE and AC is not 0.

 The coordinates of D and E were found using the Distance between Two Points Postulate