## alwaysdancing18 2 years ago Can you conclude that the quadrilateral is a parallelogram? Explain.

1. alwaysdancing18

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2. Dido525

OOps.

3. Dido525

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4. Dido525

Lets use a geometric argument.

5. alwaysdancing18

ok....

6. Dido525

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

7. Dido525

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

8. Dido525

Similarly, angle must equal angle c.

9. Dido525

If we make two triangles, Triangle abc and triangle def

10. Dido525

180-e-d must equal angle f.

11. Dido525

Are you following me so far?

12. alwaysdancing18

yes I am, I am writing this down

13. Dido525

Similarly, 180 - a -c must equal b.

14. alwaysdancing18

ok I dont understand what 180-a-c means

15. Dido525

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

16. Dido525

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

17. Dido525

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

18. alwaysdancing18

oh.. so does that mean 180 degrees has to be subtracted by angle a and c to find B? or am I completely wrong?

19. Dido525

Yes you are correct but do you understand why?

20. alwaysdancing18

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

21. Dido525

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22. Dido525

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23. Dido525

Does that make sense?

24. alwaysdancing18

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?

25. Dido525

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

26. alwaysdancing18

SAS?

27. Dido525

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.

28. Dido525

Ohh yeah, that's valid too :) .

29. Dido525

Good! :) .

30. alwaysdancing18

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

31. Dido525

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.

32. alwaysdancing18

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

33. Dido525

You are welcome :) .