Posted by sumer on Thursday, July 28, 2011 at 1:39am.
prove: the segment joining the midpoints of the two sides of a triangle is parallel to the third side. the coordinates are A(0,0)B(a,0)on the the x axis, and C(c,d), M is midpoint and the coordinates of M is (c/2,d/2) and N is also a midpoint whose coordinates are (a+c/2, d/2) Please help fill in the blanks M=(0+____/2, 0+_____/2)=(_____/2, _____/2) and then N=(______+C/2, 0+________/2)=(______+C/2, _________/2)
slope of MN = d/2 _____d/2 = _______
____________ a+c/2c/2 =________ a+c/2  c/2
slope of AB = ____________=_______=____
a a
please any help would be greatly appreciated thanks so much!!!!

geometry  Reiny, Thursday, July 28, 2011 at 8:59am
For the x of the midpoint, add the xcoordinates of the two endpoint and divide by 2, (averaging them)
So for M we get
( (0+c)/2 , (0+d)/2) = (c/2, d/2)
for N
( (a+c)/2 , (d+0)/2) = ( (a+c/2 , d/2)
slope of MN = (d/2  d/2)/((c+a)/2  c/2)
= 0/ ??? = 0
slope of AB = (00)/(a0) = 0/a = 0
so MN  AB
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