Given: Quadrilateral ABCD is a parallelogram
Prove AB is congruent to CD and BC is congruent to AD
Edit: got step 7 guys, its Triangle ABC is congruent to CDA (C, if i remember correctly) Will be back with step 2 answer.
EDIT 2: Got it guys step two is ABllCD and BCllAD and the reason is definition of a parrelelogram i hope tihs helps you'll prolly see this when its a year old lol bet money

- anonymous

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- anonymous

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## More answers

- anonymous

the obligatory will fan will medal

- anonymous

@misssunshinexxoxo

- anonymous

help pls

- anonymous

@dan815 how much do your services cost?

- dan815

okay there are some basic triangle theorems you have to know
3 main ones are
AAS, SSS, and SAS theorems that if satisfied means the 2 triangles are congruent

- anonymous

All righty

- dan815

the next is parallel lines and which angles are equal lets start there!

- anonymous

ok

- dan815

Lets first draw 2 parallel lines and see if we can find something about an intersection of a line through them

- dan815

|dw:1435329917728:dw|

- dan815

|dw:1435329932545:dw|

- anonymous

ok

- dan815

oky we know that angle 1 = angle 2 , as these are opposite angles and opposite angles have ot be equal

- dan815

we can see this very easily as angles along a straight line add up to 180

- anonymous

yes they do

- anonymous

supplementary, right?

- dan815

|dw:1435330043205:dw|

- dan815

you see how that angle in between 1 and 2, is 180 - angle 2 or 180 - angle 1

- dan815

this means angle 2 and 1 have to be the same

- dan815

tell me if you understand that

- anonymous

im following so far

- dan815

okay now you know why opposite angles are equal, lets move on

- dan815

|dw:1435330127812:dw|

- dan815

im not sure exactly how to prove that one, but take that as face value its more intuitive, it must be true kinda thing

- anonymous

ok

- anonymous

lol

- dan815

like think about it it angle 3 is not the same as angle 1

- dan815

then these lines cannot be parallel right

- dan815

beccause somewhere at some point they will intersect and form a triangle

- anonymous

correct

- dan815

okay so thats all we need to solve your question

- dan815

now lets make a parallelogram

- dan815

|dw:1435330263015:dw|

- dan815

|dw:1435330293860:dw|

- dan815

|dw:1435330340749:dw|

- dan815

these angles have to be the same here

- dan815

from the parallel lines we saw before its like this Z pattern

- anonymous

ok

- dan815

can you really see that

- anonymous

yes i can

- dan815

can you tell me what other angles have to be the same from this same idea

- anonymous

|dw:1435330489666:dw|

- dan815

yep that is right, now what does that mean about the remaining angle

- anonymous

to be honest, im not sure.

- dan815

okay lets think about it

- dan815

all angles in a triangle add upto what

- dan815

|dw:1435330606939:dw|

- anonymous

ohh 180

- anonymous

and since theres 2 in the parrelelogram its 360 degrees

- dan815

okay now u see both triangles in there have an angle that is a and angle that is b

- dan815

what is the remaining angle?

- dan815

the remaining angles have to be equal too... tell me why

- anonymous

because of the alternate exterior?

- dan815

forget that stuff, think logic

- dan815

we know all the angles add upto 180 right

- dan815

a+b+the remaining angle is 180

- anonymous

yes

- dan815

then the same remaining angle must be on the bottom too as there is an a and a b

- anonymous

ok

- dan815

so we have 3 samme angles and a side that is the same, as the diagonal is shared

- dan815

|dw:1435330902779:dw|

- dan815

so by AAS rule, these triangles are congruent

- anonymous

ok

- dan815

okay bye

- anonymous

thank you, later on today i will reward you with owl bucks for your torubles.

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