SOLUTION: 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: ΔABC Prove: The midse

Algebra.Com
Question 1040266: 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: ΔABC
Prove: The midsegment between sides Line segment AB and Line segment BC is parallel to side Line segment AC.
Draw ΔABC 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 Midpoint Formula. Point E is the midpoint of Line segment BC with coordinates of 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 Midpoint Formula. 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 Parallel Postulate.
Which statement corrects the flaw in Gina's proof?
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
It is very bad choice and very bad way to place such text in this website for discussion.

It is very difficult to read it.

If you are interested in learning on midsegment of a triangle, read the lesson The line segment joining the midpoints of two sides of a triangle in this site.

For your future studies on properties of triangle see the lesson PROPERTIES OF TRIANGLES in this site.

For your future studies on Planimetry see the lesson GEOMETRY - YOUR ONLINE TEXTBOOK in this site.


And the last notice.

If you want to learn Geometry, Math and so on, use only good sources.

Don't spend your time searching for nothing in mountains of trash.


RELATED QUESTIONS

Gina wrote the following paragraph to prove that the segment joining the midpoints of two (answered by mykasha)
Prove that the line joining the midpoints of consecutive sides of a quadrilateral is a... (answered by ikleyn)
Give a detailed proof of the following fact: The line segment joining the midpoints of... (answered by solver91311)
Prove that the triangle formed by joining the midpoints of the sides of an isosceles... (answered by mananth)
Please help! Problem: "Prove that the figure formed by connecting the midpoints of the... (answered by venugopalramana)
prove the following using coordinate geometry: The segments joining the midpoints of the... (answered by Edwin McCravy)
Find the length of the segment joining the two midpoints of the sides of the triangle if... (answered by ikleyn)
In a triangle, a segment is drawn joining the midpoint of two sides. What is true about... (answered by MathLover1)
The vertices of a triangle are at ( 4, 5 ), ( -7, -6 ) and ( 10, -3 ). Show that the line (answered by math_tutor2020)