Question

Anyone really good at explaining Two-Column Proofs?

Answer 1

of what ?

Answer 2

Figures, you have to prove them congruent but I don't understand what information to eave out and include. Nor don't I understand how many rows there needs to be

Answer 3

More specifically something like this.

Answer 4

Well the number of rows is the number of statements you need to prove the conclusion. The second column for each row is just your justification for that row, usually it will reference a theorem or another row. Is that kind of what you were asking?

Answer 5

a two-column proof written in sentences. However, since it is easier to leave steps out when writing a paragraph proof, we'll learn the two-column method.

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column. Every step of the proof (that is, every conclusion that is made) is a row in the two-column proof.

Answer 6

kind of, only i don't quite understand it still. Is it possible to have multiple possible answers? Like can i just put on the right side "The definition of a(n) [BLANK]"?

Answer 7

Okay, now I have a question about the fifth row. I have NO idea what to answer. and in the bottom row, idk what they are looking for.

Answer 8

So for a lot of proofs there will be more than one right answer, because you're basically formulating an argument to prove a statement and the intricacies of that argument may differ but still be sound and valid. However, in this case, because they've already given you the proof and you're filling in the blanks, I think the answers are going to be pretty limited.

Specifically in the fifth row they have identified that two angles are alternate exterior angles (in the row above) and from that fact are deducing that they must be congruent. So your justification for that is probably a theorem you have that alternate exterior angles are congruent. Does that make sense?

Answer 9

Yes it does! thankyou!(: The next proof I have to do is very difficult and I'm unsure what to do after the "given" statements. :/ I'll attach the file in a moment

Answer 10

I need to completely make a column, will it end up being 7 rows like the other?

Answer 11

Well it might but it doesn't have to. Instead of thinking about it in columns and rows, think about how you might demonstrate that the conclusion is true, and then we can break it down into steps.

Answer 12

okay ): help?

Answer 13

Sure, I don't want to say too much because I'm not sure what theorem's/etc are available to you to use in your class and I don't want to mislead you. but there seems to be a pretty simple way to approach this.

First of all, write down what your given, because odds are you'll need to use it.

In this case, we know that EGF is 60 and AGF is 90, right?

Answer 14

Now the measure of AGD is 180 degrees supposing it is a straight line. So what does that tell us about the measure of angle EGD?

Answer 15

hint: EGD is supplementary to AGE whose measure is the sum of EGF and AGF

Answer 16

you're dealing with a blonde here ... :/ thankyou for your patience. ): but i find all of this very confusing

Answer 17

no prob's. Supplementary angles sum to 180 degrees. So the angle we are interested in is supplementary to two angles that are 60 and 90 degrees, right? Thus, the sum of the three angles is 180 degrees and our angle is 180-60-90=30.

Answer 18

If I wanted to break that down into steps I would say
1) mEGF is 60 (given)
2) mAGF is 90 (given)
3) mAGE is 150 (because it is the sum of 1 and 2)
4)so mEGD is 30 (because it is supplementary with mAGE and 180-150 is 30).

Answer 19

Does that make sense so far?

Answer 20

yes, but the proofs ask for the theorems or postulates. It's been a while since I've done this stuff and I of course have no text books and only have 50+ pages on an online document.

Answer 21

got you not sure i can help you there since it's been awhile for me too. I know there's a theorem for 4) that states that supplementary angles add to 180 degrees. 3) is true but I'm not sure what the theorem would be. Maybe something about the measure of adjacent angles is the sum of their angles.

Answer 22

just fyi there's one more step 5) which says that EGD AGB are vertical angles and hence congruent

Answer 23

actually, I do have a text book. I got kicked out of school & I forgot they sent home a textbook & never asked for it back

Answer 24

haha nice
I would check the book for some more official sounding names, but all those reasons are sound and the statements follow.

Answer 25

I guess i should know what i'm looking for before diving into a book aha...

Answer 26

yeah, look for a theorem about the sum of adjacent angles, one about the sum of supplementary angles, and one about vertical angles being congruent. That should do it.

Answer 27

I found a chapter called "Reasoning and Proof" worth a shot?

Answer 28

yeah, it might give you a good overview of the proof process. I would guess for this specific proof you're actually going to be looking for a chapter on angle relationships

Answer 29

Properties of equality is what the proofs are looking for!(:

Answer 30

nice

Answer 31

i think..