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deff fn [24]
3 years ago
9

Prove ABCD is a parallelogram by showing both pairs of opposite sides are parallel. please Show All Work! Thanks!!

Mathematics
2 answers:
katrin [286]3 years ago
8 0

Answer:

Step-by-step explanation:

To prove this we should first make a little representation to get an idea of how will proceed to work .

To solve it we should use vectors so the first step is to identify this vectors :

  • we have four points : A/B/C/D
  1. A(-2,-4)
  2. B(1,2)
  3. C(2,10)
  4. D(-1,4)
  • VECTOR AB WITH VECTOR DC
  • VECTOR AD WITH VECTOR BC

NOW LET'S IDENTIFY 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)

We get :

  • VECTOR AB (3,6) VECTOR DC (3,6)
  • VECTOR AD (1,8) VECTOR BC  (1,8)

We notice that the opposite ones have the same coordinates so the edges are parallel .

If we want to check more we can calculate the lenghts :

  • AB=\sqrt{3^{2}+6^{2}  }     DC=\sqrt{3^{2}+6^{2}  }

So AB=DC

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

So AD=BC

SO ABCD IS A PARALLELOGRAM

nadezda [96]3 years ago
7 0

Answer:

Here You Go! I'm not really sure about this one but i tried.

Step-by-step explanation:

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