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One moment, need to screenshot!

two angles are supplementary, iff they add to 180°

Okay..

iff \(\angle FEA\) is supplementary to \(\angle HGD\)
\[\text m\angle FEA+\text m\angle HGD = 180°\]

Wait.. I don't understand...

consider the first option, does it agree?

Yes?..

What is it that you don't understand?

Just the overall question. It's weird.
It's not option A or B is what I'm getting so far, right?

(check carefully now)
Does:
\[\text m\angle FEA+\text m\angle HGD = 180°\]
agree with option one?

It.. it's not 180, I think..?

there are only two angles to consider;
the big one : ∠FEB = ∠HGD
and the little angle : ∠FEA = ∠HGC

where any pair, of one big and one little angle, will always add to 180°,

So A is not true, which makes it the right answer?

but why is A not true?

Because the angles are too big, right?

yeah,
big angle + big angle ≠ 180°

Okay, I kinda get it...

What about this problem?

(unless all the angles were exactly 90°, which doesn't fit the diagram )

can you find the angles in the first option on the diagram?

|dw:1434794031396:dw|

In the first one, they look equal to me.. unless I am not understanding this properly.

Alternate, I think..

u can't see any angles alternate to angle EIA

So it's the first option, yes?

|dw:1434794616346:dw|

|dw:1434794679515:dw|

Oh, so they're opposite angles?.. so they are congruent.

Yes!

Then there's this... I was always bad at these in class.

what is the difference between line 3, and line 4?

They're adding segments together and asking if they're congruent.

3. AB + BC + CD = CD + DE + EF
4. AB + BC = DE + EF
What has happened ?

They're.. substituting I think?

what has been substituted for what?

The concurrency, I think.

*congruent

nope

3. AB + BC + CD = CD + DE + EF
4. AB + BC = DE + EF
how are theses lines different ?

Uh.. I have no legitimate clue.

read line 3. and then read line 4.

It removed two of the segments, I see that much.. :/

@TillLindemann no CD

yeas, CD has been taken away from both sides of the equation

Okay.. so it's asking if they're still congruent without them, no?

So would it not be D?..

So D, yes? I'm so confused.

another word for take-away or minusing, is subtraction

Wait. So.. It's C?

does that makes sense now?

Yes, because they removed one of the segments, it makes it the Subtraction property, right?

This is one of those ones where you have to do a bunch of weird nitpicking to get the correct answer...

Not sure, but I think it's linear and angle BED...

Er, not angle.. but.. you get what I'm trying to say.

what is the linear angle theorem?

|dw:1434796331473:dw|
This right?

that might be the linear angle theorem, but i don't see how it relates to this question

you got \(\angle AEC \cong \angle BED \) (by the vertical angle theorem) right

the linear angle theorem is not about congruence (equality), it is a about supplementary angles

Okay, but?...

compare the two lines of this question

Is it vertical?..

yer

And still angle BED, right?

yep they are vertically opposite angles in each case

This one is really long as well.

what do you think

Well, I've had this question multiple times before and I always get it wrong...

i'm not going to tell you what the answer is

I know that, but I haven't a single clue on how to find it..

Which parts of the closed passage do you not understand exactly?

Well, this whole section really.

Yes, I think the first answer to the big question is transitive..

i think that is right,
what about the next one

Vertical maybe...

vertical angles are congrunent (not supplementary )

It's not linear, right?.. or is it?

Which do you think ?

|dw:1434798665055:dw|

I think it's linear but I have no clue.. could be the congruent supplements one though.

the congruent supplements theorem involves three angles
you have plenty of clues

So then it is linear, no?

why not, eh?

Yep substitution is right

I think it's the first option...

that doesn't prove the what you are trying to prove

the last line of the proof should say something about what you are trying to prove

The congruent supplement one, yeah.. I think that's the right answer.

Now I feel like it's more option D...

B?...

stop guessing

Well I don't understand.

\[\angle 3\cong \cdots\cong\angle6, ...\]

That doesn't help me.

Because there is no option with 3 and 6 in it at the same time.

you have
\[\angle 3\cong \angle 7, ...\]
you need
\[\angle 7\cong\angle6, ...\]

So it'd D.

Um, yes it is.

Thank you. That's all I needed for now. Thanks so much for helping.