The prove that the angle ABCD is said to be a parallelogram that shows both pairs of opposite sides as parallel figure is given below.
What is the parallelogram about?
The four points in the shape above are : A, B, C, D.
Where
A = (-2,-4)
B = (1,2)
C = (2,10)
D = (-1,4)
We place or sit vector AB with vector DC and vector AD with vector BC
and so we find and place their coordinates.
vector AB (1-(-2), 2-(-4))
vector DC (2-(-1),10-4)
vector AD (-1-(-2), 4-(-4))
vector BC (2-1,10-2)
So we obtained:
vector AB (3,6)
vector DC (3,6)
vector AD (1,8)
vector BC (1,8)
Next step is to calculate for the lengths :
AB= [tex]\sqrt{3^{2} + 6^{2} }[/tex] DC= [tex]\sqrt{3^{2} + 6^{2} }[/tex]
Thus, AB = DC
AD = [tex]\sqrt{1^{2} + 8^{2} }[/tex] BC =[tex]\sqrt{1^{2} + 8^{2} }[/tex]
Hence one can say that AD is equal to BC.
Therefore, angle ABCD IS known to be a parallelogram .
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