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 Line segment AB and Line segment BC is parallel to side Line segment 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). Point D is the midpoint of Line segment AB with coordinates at Ordered pair the quantity 0 plus x sub 1, divided by 2; the quantity 0 plus y sub 1, divided by 2 by the slop

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 Line segment AB and Line segment BC is parallel to side Line segment 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). Point D is the midpoint of Line segment AB with coordinates at Ordered pair the quantity 0 plus x sub 1, divided by 2; the quantity 0 plus y sub 1, divided by 2 by the slop

anonymous · Answer

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