Question 622903: 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 Triangle 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). Construct point D so it is the midpoint of Line segment AB . Point D has 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 Distance between Two Points Postulate. Construct point E so it is the midpoint of Line segment BC . The ordered pair of point E is Ordered pair the quantity x sub 1 plus x sub 2 divided by 2; the quantity 0 plus y sub 1 divided by 2 by the Distance between Two Points Postulate. The slope of Line segment DE is found to be 0 through the application of the slope formula: The difference of y sub 2 and y sub 1, divided by the difference of x sub 2 and x sub 1 is equal to the difference of the quantity 0 plus y sub 1, divided by 2, and the quantity 0 plus y sub 1, divided by 2, divided by the difference of the quantity x sub 1 plus x sub 2, divided by 2 and the quantity 0 plus x sub 1, divided by 2 is equal to 0 divided by the quantity x sub 2 divided by 2 is equal to 0 When the slope formula is applied to Line segment AC the difference between y sub 2 and y sub 1, divided by the difference of x sub 2 and x sub 1 is equal to the difference of 0 and 0, divided by the difference of x sub 2 and 0 is equal to 0 divided by x sub 2 is equal to 0 , its slope is also 0. Since the slope of Line segment DE and Line segment AC are identical, Line segment DE and Line segment AC are parallel by the definition of parallel lines.
What is the flaw in Gina’s proof?
Answer by mykasha(37)   (Show Source):
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