Please Please help me with this easy problem! I will fan and medal!

Question

anonymous · Answer

What problem?

anonymous · Answer

Given:AB=CD, AD=CB
Prove: Triangle ABD=Triangle BCD

anonymous · Answer

I need help writing a proof for this!

anonymous · Answer

@Moofish

anonymous · Answer

@sleepyjess  Can you help?

sleepyjess · Answer

Do you have a picture?

anonymous · Answer

@sleepyjess  Yea hold on

anonymous · Answer

attachment

anonymous · Answer

@sleepyjess

sleepyjess · Answer

brb

anonymous · Answer

@sleepyjess Okay.. :)

sleepyjess · Answer

Okay, I'm back

sleepyjess · Answer

Do you have to use all 4 statement/reason slots?

sleepyjess · Answer

This can really be completely done by using 2 of the slots...

anonymous · Answer

@sleepyjess I believe you are suppose to use all four but the first one would be the given statement

sleepyjess · Answer

True true, actually the first 2 would be, since only one statement goes in each slot

anonymous · Answer

Okay and so what would then be the other two slots?

sleepyjess · Answer

Okay, so we have 
AB $\cong$ CD | Given
AD $\cong$ CB | Given
Now, what is the other side of both triangles? Hint: They are the same line!

anonymous · Answer

Ummm would it be BD?

anonymous · Answer

@sleepyjess

sleepyjess · Answer

Yes! So the third slot would be 
BD $\cong$ BD | Reflexive Property of Congruence

sleepyjess · Answer

Now, we can prove the triangles congruent by SSS, Side-Side-Side

anonymous · Answer

Wait so wouldnt BD reasoning be SSS? Not Reflexive Property Of Congruence?

sleepyjess · Answer

Well, the triangles being congruent would be SSS

sleepyjess · Answer

BD $\cong$ BD is like saying that a + b = a + b

anonymous · Answer

Ohhh Okay that makes perfect sense :) Thanks for explaining that. Sorry Im so horrible at geometry! So what would the next blank be?

sleepyjess · Answer

No problem! The last slot would be ABD $\cong$ BCD | SSS

anonymous · Answer

Of course! I knew that :) Thank you again so much!

anonymous · Answer

You really helped break this down for me! Could you help me with one more problem?

anonymous · Answer

@sleepyjess

sleepyjess · Answer

Sorry, was afk for a minute :P
No problem! And sure :)

anonymous · Answer

@sleepyjess No problem! Thought my computer might be freezing lol :)

anonymous · Answer

attachment

sleepyjess · Answer

haha nope :P

anonymous · Answer

I just need to complete the last blank

sleepyjess · Answer

Have you ever heard of $\color{blue}{Corresponding\: Parts\: of \: Corresponding \: Triangles\: are\: Congruent?}$

anonymous · Answer

No I dont think so :/

sleepyjess · Answer

Hmm... I'll try to explain

anonymous · Answer

I mean It makes sense that if two triangles are congruent all its parts would also be congruent

sleepyjess · Answer

On this picture, we know that they've already proven ABC $\cong$ DEF, so we know all of the sides must be congruent right?

sleepyjess · Answer

As well as all of the angles

anonymous · Answer

@sleepyjess Yes that makes perfect sense

sleepyjess · Answer

Okay, since AB and DE would line up if we put the triangles on top of each other, those would be the corresponding sides, same with BC and EF, and AC and DF

anonymous · Answer

Right so AB=DE and BC=EF and AC=DF because they are all corresponding angles

sleepyjess · Answer

Exactly!

sleepyjess · Answer

I'm not sure why you think you're bad at geometry, you catch on to new concepts so fast!

anonymous · Answer

So for the last blank I would put AB=DE because its a corresponding angle?

sleepyjess · Answer

Close, you would put CPCTC, $\bf C$orresponding $\bf P$arts of $\bf C$orresponding $\bf T$riangles are $\bf C$ongruent

anonymous · Answer

Okay :) I cant thank you enough for all the help youve given me!

sleepyjess · Answer

You're such an awesome learner! Keep up the good work :)

anonymous · Answer

@sleepyjess Aww thank you so much! You have no idea how much that really means to me!