## anonymous one year ago 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

1. anonymous

2. anonymous

3. anonymous

4. anonymous

the obligatory will fan will medal

5. anonymous

@misssunshinexxoxo

6. anonymous

help pls

7. anonymous

8. 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

9. anonymous

All righty

10. dan815

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

11. anonymous

ok

12. dan815

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

13. dan815

|dw:1435329917728:dw|

14. dan815

|dw:1435329932545:dw|

15. anonymous

ok

16. dan815

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

17. dan815

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

18. anonymous

yes they do

19. anonymous

supplementary, right?

20. dan815

|dw:1435330043205:dw|

21. dan815

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

22. dan815

this means angle 2 and 1 have to be the same

23. dan815

tell me if you understand that

24. anonymous

im following so far

25. dan815

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

26. dan815

|dw:1435330127812:dw|

27. 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

28. anonymous

ok

29. anonymous

lol

30. dan815

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

31. dan815

then these lines cannot be parallel right

32. dan815

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

33. anonymous

correct

34. dan815

okay so thats all we need to solve your question

35. dan815

now lets make a parallelogram

36. dan815

|dw:1435330263015:dw|

37. dan815

|dw:1435330293860:dw|

38. dan815

|dw:1435330340749:dw|

39. dan815

these angles have to be the same here

40. dan815

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

41. anonymous

ok

42. dan815

can you really see that

43. anonymous

yes i can

44. dan815

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

45. anonymous

|dw:1435330489666:dw|

46. dan815

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

47. anonymous

to be honest, im not sure.

48. dan815

okay lets think about it

49. dan815

all angles in a triangle add upto what

50. dan815

|dw:1435330606939:dw|

51. anonymous

ohh 180

52. anonymous

and since theres 2 in the parrelelogram its 360 degrees

53. dan815

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

54. dan815

what is the remaining angle?

55. dan815

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

56. anonymous

because of the alternate exterior?

57. dan815

forget that stuff, think logic

58. dan815

we know all the angles add upto 180 right

59. dan815

a+b+the remaining angle is 180

60. anonymous

yes

61. dan815

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

62. anonymous

ok

63. dan815

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

64. dan815

|dw:1435330902779:dw|

65. dan815

so by AAS rule, these triangles are congruent

66. anonymous

ok

67. dan815

okay bye

68. anonymous

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