Question

I am willing to do the work. Help me understand.
Provide the reasons for the proof.
Given angle 1 and angle 3 are vertical angles.
Prove angle 1 is congruent to angle 3.
I will post possible answers and graph once the question becomes active.

Answer 1

Please let me know if the writing is to small, I can type it out as we work through it.

Answer 2

can you upload a pdf instead?

Answer 3

Unfortunately I took this directly out of my online math book, so a pdf would be difficult, I can type it out though...

Answer 4

Ok what are the answer choices?

Answer 5

"I will post possible answers and graph once the question becomes active."

Answer 6

Heres the file in PDF form

Answer 7

Ah, thank you! I apologize, math nor tech is my strong point.

Answer 8

Oh ok i see the possible answer choices. Sorry didnt see that before!

Answer 9

So basically the problem asks us to fill in the 'reason' for the steps. The first one is GIVEN, but the other I'm a little hesitate to answer...

Answer 10

Can you list what you think the answers are?

Answer 11

It may take a little bit, because I want to compare them to the definitions on hand. If you don't mind waiting I would be more than happy to put my best effort in answering. Conversely, we could walk through each step, together?

Answer 12

That's fine too :)
ok so #1 what do you think it is?

Answer 13

Well, it tells us in the beginning that angle 1 and angle 3 are vertical angles so the correct answer for number one is: GIVEN.

Answer 14

Good
1) Given
ok thoughts on #2?

Answer 15

Hey, I wrote a tutorial on this if you'd like it for reference.
http://ec2-52-0-184-118.compute-1.amazonaws.com/study#/updates/562c2393e4b03f3e4763db6d

Answer 16

Could it possible be linear? As in definition of linear pair?

Answer 17

I dont think that is correct
linear pair is in the reason

Answer 18

I'm not saying your wrong at all, but for the purpose of knowledge why do you think the answer is wrong?

Answer 19

The reason says they form a linear pair it doesnt say that they equal 180 degrees

Answer 20

Duh, my goodness, how I did I not notice that?! I would like to take another go at it, if that's alright with you...

Answer 21

Go for it

Answer 22

Hold up

Answer 23

Linear pair is correct

Answer 24

Its a given.

Answer 25

So
1) Given
2) Linear

Answer 26

Ok, so the problem says that angle 1 and 2 are a linear pair, so its telling us the answer basically, right?

Answer 27

Yes

Answer 28

ok what do you think #3 is?

Answer 29

Supplementary angles postulate?
wo angles are supplementary if and only if the sum of their measures equals 180 degrees.

Answer 30

The thing is you don't have that in your word bank

Answer 31

Can you think of another definition that means the same thing? (it's in your word bank)

Answer 32

Let's begin the process of elimination:
Possible answers + definitions
Adjacent Angles
Two angles are adjacent if and only if they have a common vertex,

they share a common side and they have no common interior points.
Vertical Angles
Two angles are vertical if and only if they are the non-adjacent angles

formed by two intersecting lines.

Answer 33

This is a good way of thinking but you don't need to do all of this we know that supplementary angles add up to make 180 right?

Answer 34

Right.

Answer 35

A linear Pair also adds up to make 180 correct?

Answer 36

Yes, because linear pairs are supplementary to each other, right?

Answer 37

yes so #3 is....?

Answer 38

Linear Pair Postulate...

Answer 39

Good
now #4 your thoughts?

Answer 40

This one should be pretty straight forward

Answer 41

Based on the previous steps, I believe it is: Addition property of equality?

Answer 42

Correct =)

Answer 43

Ok so far so good
#5?

Answer 44

Could #5 be substitution property of equality?

Answer 45

I agree with that

Answer 46

Do you understand why?

Answer 47

Let's see, in #3 we learned that angle 1 and 2 are equal to 180 as well as angle 2 and 3. #4 further reinforced this, but now we see that angle 2 is both equations and thus do the information gathered in #3, very likely has the same degree. It is safe to assume, or replace in #5. If this is incorrect, please explain. I'm here to learn!

Answer 48

#5 is indeed substitution property of equality
"Subtraction Property of Equality: States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal. For example: If 5 = 5, then 5 - 2 = 5 - 2."
The given is that they subtracted m<2 from both sides which canceled them out and now are left with m<1 is congruent to m<3
Understood?

Answer 49

Yes, I understand!

Answer 50

And finally #6 thoughts?

Answer 51

Well, it says in the beginning that angle 1 and angle 3 are congruent, so it could be given, but its asks for a definition. This makes me want to say 'congruent', but it doesn't sound right verbally, it would make more sense if it said 'congruence'. I feel slightly put off by the other answers...

Answer 52

Well this isn't english ;p its math it doesn't matter that is correct though =) the sign is what tells you and it is a given.
Ok so to sum it up
1) Given (stated)
2) Linear (stated)
3) Linear Pair (These add up to make 180, the linear pair theorem is used when 2 angles form a linear pair, are supplementary, and add up to make 180)
4) Addition Property of equality( if a=c then a+c=b+c)
5) substitution property of equality (if a=c then a-c=b-c)
6) Congruent (the sign is a given. )

Answer 53

Yes, I suppose your right :). I agree with all of our answers. Thank you for your time and effort! I will award you a medal.

Answer 54

Thank you and welcome to openstudy! =) I hope I helped!
Also one mistake...
subtraction Property of equality= if a=b then a-c=b
i kept reading it as substitution sorry!
But all the answers are correct ^-^
Thanks for participating!