Prove ABCD is a parallelogram by showing both pairs of opposite sides are parallel, given the following points. Show all work!!!

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2 years ago

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bearhunter [10] · Answer 1 · 2023-02-22T06:41:41+03:00

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.

<h3>What is the parallelogram about?</h3>

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= $\sqrt{3^{2} + 6^{2} }$ DC= $\sqrt{3^{2} + 6^{2} }$

Thus, AB = DC

AD = $\sqrt{1^{2} + 8^{2} }$ BC = $\sqrt{1^{2} + 8^{2} }$

Hence one can say that AD is equal to BC.

Therefore, angle ABCD IS known to be a parallelogram .

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