alwaysdancing18
Can you conclude that the quadrilateral is a parallelogram? Explain.
Delete
Share
This Question is Closed
alwaysdancing18
Best Response
You've already chosen the best response.
1
|dw:1355467239515:dw|
Dido525
Best Response
You've already chosen the best response.
1
OOps.
Dido525
Best Response
You've already chosen the best response.
1
|dw:1355456638221:dw|
Dido525
Best Response
You've already chosen the best response.
1
Lets use a geometric argument.
alwaysdancing18
Best Response
You've already chosen the best response.
1
ok....
Dido525
Best Response
You've already chosen the best response.
1
If we draw a line such it it intersects two sides.
Dido525
Best Response
You've already chosen the best response.
1
Since the lengths on the opposite sides are the same, according to the parallel lines theorem, angle a must equal angle d.
Dido525
Best Response
You've already chosen the best response.
1
Similarly, angle must equal angle c.
Dido525
Best Response
You've already chosen the best response.
1
If we make two triangles, Triangle abc and triangle def
Dido525
Best Response
You've already chosen the best response.
1
180-e-d must equal angle f.
Dido525
Best Response
You've already chosen the best response.
1
Are you following me so far?
alwaysdancing18
Best Response
You've already chosen the best response.
1
yes I am, I am writing this down
Dido525
Best Response
You've already chosen the best response.
1
Similarly, 180 - a -c must equal b.
alwaysdancing18
Best Response
You've already chosen the best response.
1
ok I dont understand what 180-a-c means
Dido525
Best Response
You've already chosen the best response.
1
Since a = d and c = e , therefore we can conclude f equal b.
Dido525
Best Response
You've already chosen the best response.
1
I mean I am subtracting going: 180 degrees - angle a - angle c.
Dido525
Best Response
You've already chosen the best response.
1
Because in a triangle there is 180 degrees. Do you understand or shall I explain more?
alwaysdancing18
Best Response
You've already chosen the best response.
1
oh.. so does that mean 180 degrees has to be subtracted by angle a and c to find B? or am I completely wrong?
Dido525
Best Response
You've already chosen the best response.
1
Yes you are correct but do you understand why?
alwaysdancing18
Best Response
You've already chosen the best response.
1
because.... nope I got nothing... I just remember thats a rule somewhere right?
Dido525
Best Response
You've already chosen the best response.
1
|dw:1355457201086:dw|
Dido525
Best Response
You've already chosen the best response.
1
|dw:1355457242628:dw|
Dido525
Best Response
You've already chosen the best response.
1
Does that make sense?
alwaysdancing18
Best Response
You've already chosen the best response.
1
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?
Dido525
Best Response
You've already chosen the best response.
1
yeah okay, you could reason it that way too :P . But you had to prove they were equal first ;) .
alwaysdancing18
Best Response
You've already chosen the best response.
1
SAS?
Dido525
Best Response
You've already chosen the best response.
1
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.
Dido525
Best Response
You've already chosen the best response.
1
Ohh yeah, that's valid too :) .
Dido525
Best Response
You've already chosen the best response.
1
Good! :) .
alwaysdancing18
Best Response
You've already chosen the best response.
1
so to answer the question how do I conclude its a parallelogram?
Dido525
Best Response
You've already chosen the best response.
1
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.
alwaysdancing18
Best Response
You've already chosen the best response.
1
Thank you so much for that. You were very patient and kind. I will remember this!! Thanks. :D
Dido525
Best Response
You've already chosen the best response.
1
You are welcome :) .