how do u show that ABCD is a parallelogram

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how do u show that ABCD is a parallelogram

Mathematics
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find the length of AD and BC first
how im i supposed to do that @mathmath333
|dw:1440709546470:dw| use pythagorus for AD
ok
  • phi
there are 2 ways: show opposite sides have the same length (use the "distance formula") or show opposite sides have the same slope finding the slope is probably less work. to do either way, you first need the (x,y) coords of each corner.
  • phi
Here are the 4 points A (0,4) B (5,6) C (6,2) D (1,0) now show the slopes of AB and CD are the same can you do that ? (remember slope is change in y divided by change in x)
im i suppose to divide 0,4 @phi
nevermind
  • phi
do you remember how to find the slope between (0,4) and (5,6) ?
i have to subtract 4 and 6
then subtract 0 and 5 and divided???
is the slope 2/5 @phi
  • phi
yes. the side AB has slope 2/5 the opposite side is CD find the slope between points C and D
5/2
  • phi
you should get 2/5 . remember it is change in y divided by change in x (6,2) (1,0)
ooo ok
do i do the same for number 74
  • phi
you are not done yet. you also have to show the sides AD and BC have the same slope (opposite sides have the same slope) so far you showed sides AB and CD have the same slope. now do AD and BC
slope for AD is 1/4
  • phi
close but not 1/4 . also notice it should be negative (the line slopes down)
1/-4
  • phi
show your work
  • phi
what is change in y? what is change in x ?
-1/4
0,4 1,0 0 minus 1 is -1 4 minus 0 is 4
  • phi
ok, and which is change in y
  • phi
remember the points are (x,y) pairs in other words, 4 - 0 is the change in y the slope will be (4-0)/(0-1) = 4 / -1 = -4
  • phi
finally show line BD has slope -4
  • phi
for Q74, show line LM has slope m and line MN has slope -1/m (flipped and negated)
thx

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