anonymous
  • anonymous
Can you conclude that the quadrilateral is a parallelogram? Explain.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1355467239515:dw|
anonymous
  • anonymous
OOps.
anonymous
  • anonymous
|dw:1355456638221:dw|

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More answers

anonymous
  • anonymous
Lets use a geometric argument.
anonymous
  • anonymous
ok....
anonymous
  • anonymous
If we draw a line such it it intersects two sides.
anonymous
  • anonymous
Since the lengths on the opposite sides are the same, according to the parallel lines theorem, angle a must equal angle d.
anonymous
  • anonymous
Similarly, angle must equal angle c.
anonymous
  • anonymous
If we make two triangles, Triangle abc and triangle def
anonymous
  • anonymous
180-e-d must equal angle f.
anonymous
  • anonymous
Are you following me so far?
anonymous
  • anonymous
yes I am, I am writing this down
anonymous
  • anonymous
Similarly, 180 - a -c must equal b.
anonymous
  • anonymous
ok I dont understand what 180-a-c means
anonymous
  • anonymous
Since a = d and c = e , therefore we can conclude f equal b.
anonymous
  • anonymous
I mean I am subtracting going: 180 degrees - angle a - angle c.
anonymous
  • anonymous
Because in a triangle there is 180 degrees. Do you understand or shall I explain more?
anonymous
  • anonymous
oh.. so does that mean 180 degrees has to be subtracted by angle a and c to find B? or am I completely wrong?
anonymous
  • anonymous
Yes you are correct but do you understand why?
anonymous
  • anonymous
because.... nope I got nothing... I just remember thats a rule somewhere right?
anonymous
  • anonymous
|dw:1355457201086:dw|
anonymous
  • anonymous
|dw:1355457242628:dw|
anonymous
  • anonymous
Does that make sense?
anonymous
  • anonymous
so that means both ABC and DEF are equal because they were cut equally in half. So each triangle equal 180 and both together is 360?
anonymous
  • anonymous
yeah okay, you could reason it that way too :P . But you had to prove they were equal first ;) .
anonymous
  • anonymous
SAS?
anonymous
  • anonymous
You can only prove they are equal if you cut the quadrilateral in half like I said. THen you had to prove that I did cut it in half by proving all the angles were the same.
anonymous
  • anonymous
Ohh yeah, that's valid too :) .
anonymous
  • anonymous
Good! :) .
anonymous
  • anonymous
so to answer the question how do I conclude its a parallelogram?
anonymous
  • anonymous
Now since you have proved all the angles are the same on opposite sides, you can conclude that this quadrilateral in indeed a parralelogram because the opposite sides have the same length and the angles on opposite sides of each other are the same as well.
anonymous
  • anonymous
Thank you so much for that. You were very patient and kind. I will remember this!! Thanks. :D
anonymous
  • anonymous
You are welcome :) .

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