Question

About proofs..
Given: Quadrilateral ABCD, line segment AD is congruent to line segment BC and angle DAE is congruent to angle BCE
Prove: Triangle AEF is congruent to triangle CEG

Someone please help me out with statements and reasons, totally lost. (:

Answer 1

Ok.
First we draw a picture.

Answer 2

I have the picture, it was given. This is from a regents review.

Answer 3

Well, you should provide the picture, because E comes out of nowhere.

Answer 4

Give me a minute, I'll upload one.

Answer 5

Picture

Answer 6

ABCD is a parallelogram because of the alternate interior angles

Answer 7

in a parallelogram, diagonals bisect each other.

Answer 8

due to ASA congruence thesetwo triangles are congruent.

Answer 9

Im confused.. are those my statements or reasons along with?
I'm a hopeless case when it comes to proofs..sorry to frustrate you..

Answer 10

in triangles AEF and CEG
Angle DAE = Angle BCE ( given)
AE = EC (given)
Angle FEA = Angle GEC ( vertically opposite)

therefore triangles AEF and CEG are congruent by A A S test

The FE = EG corresponding sides in congruent triangles

Answer 11

*ASA

Answer 12

@campbell_st , that's not correct...

Answer 13

in triangles AEF and CEG
Angle DAE = Angle BCE ( given)
AE = EC

Angle FEA = Angle GEC ( vertically opposite)
therefore triangles AEF and CEG are congruent by A S A test
The FE = EG corresponding sides in congruent triangles

Answer 14

My teacher mentioned that you use Alternate Interior Angles to prove parallel lines...

Answer 15

AE=EC is because ABCD is a parallelogram

Answer 16

ABCD is a parallelogram because of the angles given.

Answer 17

(one pair of congruent and parallel sides makes a parallelogram)

Answer 18

you're not asking to prove parallel lines
you're asked to prove congruency

and with the proves ASA and AAS are the same proves... its showing 2 angles ( and subsequently the 3rd) and a side in 1 triangle are congruent to another.

Answer 19

Uhm, no.

Answer 20

I understand what I'm trying to prove and need to end up using a triangle congruence theorem, but to get to that, apparently I did it wrong the first time.

Answer 21

you can say AD and BC are parallel bot there is no information about AB and CD to say they are parallel.... the quadrilateral could be a trapezium...

Answer 22

AE = EC (given) is wrong.

Answer 23

That's not given dude.

Answer 24

That's proved

Answer 25

by showing quadrilateral ABCD is a parallelogram, and that a parallelogram's diagonals bisect each other.

Answer 26

if you use my solution us have don it correctly... its just that it doesn't agree with you're teacher's solution.... perhaps because he wanted a specific method rather then the more lateral solution of proving congruency... by any method

Answer 27

you can say AD and BC are parallel bot there is no information about AB and CD to say they are parallel.... the quadrilateral could be a trapezium...
COmpletely wrong
One pair of parallel and congruent sides detemnes a parallelogram.

Answer 28

en.wikipedia.org/wiki/Parallelogram#Characterizations

Answer 29

Read wikipedia before you say that it isn't a parallelogram.

Answer 30

well good luck

Answer 31

And, @campbell_st , your proof is completely wrong.

Answer 32

inkyvoyd- i'm agreeing with your explanations only because it sounds as how my teacher would've put it. Now I ask of you if you could easily write out the statements and reason in a charted way such as
Statements | Reasons
______________________________________
1. Quadrilateral ABCD ... etc | 1. Given

Answer 33

AD is congruent to line segment BC
It says absolutely nothing about AE and EC

Answer 34

Alright, I'm going to just prove that AE is congruent to EC, because that's all that we are missing.

Answer 35

1. AD is parallel to BC (Converse of the alternate interior angles theorem)
2. angle DAE is congruent to angle BCE (Given)
3. Quadrilateral ABCD is a parallelogram (One set of congruent and parallel sides determines a parallelogram) #This is usually assumed as "common knowledge" in geometry, so you don't have to prove it, unless specifically requested.
4. DB bisects AC (Properties of a parallelogram)
5. AE is congruent to EC (definition of bisection)

Answer 36

@deckedinchrome , there you go, I am so NOT typing that again, waht a pain lol

Answer 37

here is the proof

Angle DAE = Angle BCA ( given)

therefore AD is parallel to CB

prove congrency in triangles ADE and BCE
Angle DAE = Angle BCE (given)
DA = CB (given)
Angle ADE = Angle CBE ( interior alt angles AD//CB)

Triangles are congruent by ASA test
then AE = CE corresponding angles in congruent triangles


so in Triangles FEA and CEG

angle FAE = angle CGE (given)
Angle FEA = angle CEG ( vertically opposite)
AE = CE (proved above)

therefore triangles ADE and BCE are congruent by ASA test..,.

QED

Answer 38

Well, that works too 0.o

Answer 39

oops AE = EC corresponding sides in congruent triangles

Answer 40

Techinically we just did the same proof...

Answer 41

You just proved that ABCD is a parallelogram, while I assumed that it was..

Answer 42

i.e. your answer is better than mine, but mine would get full credit as well.

Answer 43

the question says prove.... not assume...

Answer 44

What do you mean by "converse of the alternate interior theorem"?

Answer 45

No.

Answer 46

It is common knowledge that parallelograms are determined by one pair of parallel congruent sides

Answer 47

Don't tell me it isn't, I learned that in both America and Taiwan, a total of three times. I also self studied it.

Answer 48

And, converse means

Answer 49

if a, then b
converse: if b, then a

Answer 50

Converses are not always true, but for the alternate interior angle theorem, the converse is valid as well as the original statement.

Answer 51

it shows AD and CB are parallel... thats all.... but good luck with your geomerty

Answer 52

No, AD and CB are congruent.

Answer 53

Congruent+parallel means it is a parallelogram.

Answer 54

Did you even read wikipedia dude?-.-

Answer 55

*congruen and parallel

Answer 56

lol.... well whatever you believe.... its proven.... simple as that

Answer 57

Guys. quit blowing up my question with your arguments.
Also, Wikipedia is an unreliable source that can be edited by anyone.
Also: for #4 in the proof from inkyvoyd, explain properties of a parallelogram

Answer 58

Wikipedia is a reliable source when you check the citations.

Answer 59

That particular block just happens to have 2 (yes -.-) citations.

Answer 60

@Hero , please explain what I'm trying to say, as well as help decked here out, before I rage quit.

Answer 61

(my proof, not wikipedia's credibility lool)

Answer 62

And @deckedinchrome , that part is also common knowledge. Go read wikipedia for proof,

Answer 63

en.wikipedia.org/wiki/Parallelogram#Proof that diagonals bisect each other

Answer 64

this stuff all depends on you motivation... I find it easier to have good basics that can be applied to any question than relying on a memory full of facts i may or may not use

Answer 65

Well, I find it good to have both.

Answer 66

Asian math has trained me to be able to rely on memory, because the problems that we get can get much much harder

Answer 67

Alright. Nevermind. You're frustrated as me because I'm clearly a dumb blonde in geometry. Your reasons are too logical and your knowledge base is clearly that of much higher than mine. I just bullpelletted my way through the proof, and we'll see how it goes. Thanks for the help.

Answer 68

hard to the point that it might be 7 or 8 steps of "basic" knowledge. if you use memorization, it becomes maybe 3 or 4 steps. STill hard, but much faster.

Answer 69

@deckedinchrome , campbell provided a valid proof as well.

Answer 70

I just don't like him lool

Answer 71

lol... good luck to you... and close the question

Answer 72

Not yet.

Answer 73

Hero is going to help you out.

Answer 74

At least, I hope he will.

Answer 75

If you're studying for Geometry Regents exams, here's a resource that might help.

http://www.youtube.com/playlist?list=PLAA216E5D8E78F8FD&feature=plcp

Answer 76

(I assume that decked has been thoroughly trolled)