Can you conclude that the quadrilateral is a parallelogram? Explain.

- anonymous

Can you conclude that the quadrilateral is a parallelogram? Explain.

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- anonymous

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- anonymous

OOps.

- anonymous

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## More answers

- anonymous

Lets use a geometric argument.

- anonymous

ok....

- anonymous

If we draw a line such it it intersects two sides.

- anonymous

Since the lengths on the opposite sides are the same, according to the parallel lines theorem, angle a must equal angle d.

- anonymous

Similarly, angle must equal angle c.

- anonymous

If we make two triangles, Triangle abc and triangle def

- anonymous

180-e-d must equal angle f.

- anonymous

Are you following me so far?

- anonymous

yes I am, I am writing this down

- anonymous

Similarly, 180 - a -c must equal b.

- anonymous

ok I dont understand what 180-a-c means

- anonymous

Since a = d and c = e , therefore we can conclude f equal b.

- anonymous

I mean I am subtracting going: 180 degrees - angle a - angle c.

- anonymous

Because in a triangle there is 180 degrees. Do you understand or shall I explain more?

- 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

Yes you are correct but do you understand why?

- anonymous

because.... nope I got nothing... I just remember thats a rule somewhere right?

- anonymous

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- anonymous

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- anonymous

Does that make sense?

- 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

yeah okay, you could reason it that way too :P . But you had to prove they were equal first ;) .

- anonymous

SAS?

- 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

Ohh yeah, that's valid too :) .

- anonymous

Good! :) .

- anonymous

so to answer the question how do I conclude its a parallelogram?

- 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

Thank you so much for that. You were very patient and kind. I will remember this!! Thanks. :D

- anonymous

You are welcome :) .

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