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 .

Answer 1

parallel to side ac

Answer 2

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). Construct point D so it is the midpoint of . Point D has coordinates at by the Distance between Two Points Postulate. Construct point E so it is the midpoint of . The ordered pair of point E is 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

Answer 3

what is the flaw in ginas proof
The slope of segments DE and AC is not 0.

Segments DE and AC are parallel by construction.

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

Gina cannot construct the midpoint of a segment.

Answer 4

these are it i think there in order from the paragraph
http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/1001/1001_G4_Q11b.gif

Answer 5

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/1001/1001_G4_Q11d.gif

Answer 6

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/1001/1001_G4_Q11f.gif

Answer 7

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/1001/1001_G4_Q11h.gif