Proof: Median of Trapezoid is Parallel

Let's prove the following theorem:

if the y coordinate of point Z = b and the y coordinate of point Y = b and the y coordinate of point W = 0 and the y coordinate of point X = 0 and S is the midpoint of line WZ and T is the midpoint of line XY and not((the x coordinate of point T) - (the x coordinate of point S) = 0) and not((the x coordinate of point X) - (the x coordinate of point W) = 0), then ST || WX

Proof:

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Given

1	the y coordinate of point Z = b
2	the y coordinate of point Y = b
3	the y coordinate of point W = 0
4	the y coordinate of point X = 0
5	S is the midpoint of line WZ
6	T is the midpoint of line XY
7	not((the x coordinate of point T) - (the x coordinate of point S) = 0)
8	not((the x coordinate of point X) - (the x coordinate of point W) = 0)

Proof Table

Comments

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#	Claim	Reason
1	the y coordinate of point T = ((the y coordinate of point X) + (the y coordinate of point Y)) / 2	if T is the midpoint of line XY, then the y coordinate of point T = ((the y coordinate of point X) + (the y coordinate of point Y)) / 2 (Midpoint is Halfway 2)
2	the y coordinate of point T = b / 2	if the y coordinate of point T = ((the y coordinate of point X) + (the y coordinate of point Y)) / 2 and the y coordinate of point X = 0 and the y coordinate of point Y = b, then the y coordinate of point T = b / 2 (Algebra Example)
3	the y coordinate of point S = ((the y coordinate of point W) + (the y coordinate of point Z)) / 2	if S is the midpoint of line WZ, then the y coordinate of point S = ((the y coordinate of point W) + (the y coordinate of point Z)) / 2 (Midpoint is Halfway 2)
4	the y coordinate of point S = b / 2	if the y coordinate of point S = ((the y coordinate of point W) + (the y coordinate of point Z)) / 2 and the y coordinate of point W = 0 and the y coordinate of point Z = b, then the y coordinate of point S = b / 2 (Algebra Example)
5	slope of line ST = ((the y coordinate of point T) - (the y coordinate of point S)) / ((the x coordinate of point T) - (the x coordinate of point S))	slope of line ST = ((the y coordinate of point T) - (the y coordinate of point S)) / ((the x coordinate of point T) - (the x coordinate of point S)) (Slope of a Line)
6	(the y coordinate of point T) - (the y coordinate of point S) = (b / 2) - (b / 2)	if the y coordinate of point T = b / 2 and the y coordinate of point S = b / 2, then (the y coordinate of point T) - (the y coordinate of point S) = (b / 2) - (b / 2) (Subtract Same Sides)
7	(the y coordinate of point T) - (the y coordinate of point S) = 0	if (the y coordinate of point T) - (the y coordinate of point S) = (b / 2) - (b / 2), then (the y coordinate of point T) - (the y coordinate of point S) = 0 (Subtraction Example)
8	slope of line ST = 0 / ((the x coordinate of point T) - (the x coordinate of point S))	if slope of line ST = ((the y coordinate of point T) - (the y coordinate of point S)) / ((the x coordinate of point T) - (the x coordinate of point S)) and (the y coordinate of point T) - (the y coordinate of point S) = 0, then slope of line ST = 0 / ((the x coordinate of point T) - (the x coordinate of point S)) (Divide Substitute)
9	slope of line ST = 0	if slope of line ST = 0 / ((the x coordinate of point T) - (the x coordinate of point S)) and not((the x coordinate of point T) - (the x coordinate of point S) = 0), then slope of line ST = 0 (Zero Numerator Property Example)
10	slope of line WX = ((the y coordinate of point X) - (the y coordinate of point W)) / ((the x coordinate of point X) - (the x coordinate of point W))	slope of line WX = ((the y coordinate of point X) - (the y coordinate of point W)) / ((the x coordinate of point X) - (the x coordinate of point W)) (Slope of a Line)
11	(the y coordinate of point X) - (the y coordinate of point W) = 0	if the y coordinate of point X = 0 and the y coordinate of point W = 0, then (the y coordinate of point X) - (the y coordinate of point W) = 0 (Subtract Zero Example 3)
12	slope of line WX = 0 / ((the x coordinate of point X) - (the x coordinate of point W))	if slope of line WX = ((the y coordinate of point X) - (the y coordinate of point W)) / ((the x coordinate of point X) - (the x coordinate of point W)) and (the y coordinate of point X) - (the y coordinate of point W) = 0, then slope of line WX = 0 / ((the x coordinate of point X) - (the x coordinate of point W)) (Divide Substitute)
13	slope of line WX = 0	if slope of line WX = 0 / ((the x coordinate of point X) - (the x coordinate of point W)) and not((the x coordinate of point X) - (the x coordinate of point W) = 0), then slope of line WX = 0 (Zero Numerator Property Example)
14	slope of line ST = slope of line WX	if slope of line ST = 0 and slope of line WX = 0, then slope of line ST = slope of line WX (Transitive Property of Equality Variation 1)
15	ST \|\| WX	if slope of line ST = slope of line WX, then ST \|\| WX (Slope Property)