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Proofs in Algebra: Properties of Equality
 Additional Property of Equality: For all numbers a, b, and c, if a = b, then a + c = b + c
 Subtraction Property of Equality: For all numbers a, b, and c, if a = b, then a – c = b – c
 Multiplication Property of Equality: For all numbers a, b, and c, if a = b, then a × c = b × c
 Division Property of Equality: For all numbers a, b, and c, if a = b, then a/c = b/c
 Reflexive Property of Equality: For every number a, a = a
 Symmetric Property of Equality: For all numbers a and b, if a = b, then b = a
 Transitive Property of Equality: For all numbers a, b, and c, if a = b and b = c, then a = c
 Substitution Property of Equality: For all numbers a and b, if a = b, then a may be replaced by b in any equation or expression
 Distribute Property of Equality: For all numbers a, b, and c, a(b + c) = ab + ac
 One way to organize deductive reasoning is by using a twocolumn proof
Proofs in Algebra: Properties of Equality
If 4x + 5 = 9, then 4x = 4.
If a = 2y + 5 and a = b, then 2y + 5 = b.
2(m∠1 + m∠2) = 2m∠1 + 2m∠2.
If 4x + 5 = 6y + 4, then 6y + 4 = 4x + 5
If ∆ ABC ≅ ∆ DEF, and ∆ DEF ≅ ∆ MON, then ∆ ABC ≅ ∆ MON.
If 5m∠3 = 15, then m∠3 = 3.
If 2a + 3 = 5a + b, then 4a + 6 = 10a + 2b.
Given AB = 2x + 5, C is the midpoint of AB, BC = 4 Prove x = 1.5.
Statements
1.C is the midpoint of AB
2.AB = 2BC
3. 2x + 5 = 2*4 4. 2x = 3 5. x = 1.5
1. Given
2. definition of midpoint
3. substitution ( = )
4. subtraction property ( = )
5. division property ( = ).
Given m∠ABC = 5x − 5, bisect ∠ABC, m∠ABD = 25^{o}
Prove x = 11.
Statements
1. bisect ∠ABC
2. m∠ABC = 2m∠ABD
3. m∠ABC = 2*25 = 50
4. 5x − 5 = 50
5. 5x = 55
6. x = 11
1. Given
2. Bisector prostulate
3. Subst( = )
4. Subst( = )
5. Add ( = )
6. Division property of equality.
Given ∠1 and ∠2 are complementary angles, ∠2 and ∠3 are supplementary angles.
Prove m∠3 − m∠1 = 90^{o}.


*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Answer
Proofs in Algebra: Properties of Equality
Lecture Slides are screencaptured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
 Intro
 Properties of Equality
 Addition Property of Equality
 Subtraction Property of Equality
 Multiplication Property of Equality
 Division Property of Equality
 Addition Property of Equality Using Angles
 Properties of Equality, cont.
 Properties of Equality, cont.
 Two Column Proof
 Proof Example 1
 Proof Example 2
 Proof Example 3
 Extra Example 1: Name the Property of Equality
 Extra Example 2: Name the Property of Equality
 Extra Example 3: Name the Property of Equality
 Extra Example 4: Name the Property of Equality
 Intro 0:00
 Properties of Equality 0:10
 Addition Property of Equality
 Subtraction Property of Equality
 Multiplication Property of Equality
 Division Property of Equality
 Addition Property of Equality Using Angles
 Properties of Equality, cont. 4:10
 Reflexive Property of Equality
 Symmetric Property of Equality
 Transitive Property of Equality
 Properties of Equality, cont. 7:04
 Substitution Property of Equality
 Distributive Property of Equality
 Two Column Proof 9:40
 Example: Two Column Proof
 Proof Example 1 16:13
 Proof Example 2 23:49
 Proof Example 3 30:33
 Extra Example 1: Name the Property of Equality 38:07
 Extra Example 2: Name the Property of Equality 40:16
 Extra Example 3: Name the Property of Equality 41:35
 Extra Example 4: Name the Property of Equality 43:02
Geometry Online Course
Transcription: Proofs in Algebra: Properties of Equality
Welcome back to Educator.com.0000
For this lesson, we are going to talk about some properties of equality, and we are going to work on some proofs.0002
Going over some properties first: these are all properties of equality,0013
meaning that they have something to do with them equaling each other, something to do with the word "equal."0017
Now, the first one, the addition property of equality, is when you have, let's say, numbers a, b, and c.0028
If a equaled b, if the number a is the same as b, then if you add c to a, then that is the same thing as adding c to b.0039
So, if a = b, then a + c = b + c; that is the addition property of equality, because you are adding the same number to a and b, since a and b are the same.0051
And the subtraction property of equality: again, you have numbers a, b, and c.0070
a is equal to b; then, a  c is equal to b  c, as long as you subtract the same number.0076
But when you are dealing with subtraction, then it is the subtraction property.0087
But as long as you are subtracting the same number from both sides, then it is still the same.0090
You still have an equation, with equal sides.0096
The multiplication property of equality: again, you have numbers a, b, and c.0101
If a is equal to b, then a times c is equal to b times c; so again, you are multiplying the same number.0106
And the division property: for the numbers a, b, and c, if a is equal to b, then a/c is equal to b/c.0115
Now, here you have to look at this c, because you are dealing with division; so this can also be a/c = b/c.0132
This, even though it is a fraction, also means a divided by c; and when you are dealing with that,0143
since c is now the denominator, we have to keep in mind that c cannot be 0, because we can't have a 0 in the denominator.0150
So, be careful with that.0161
Now, I want to go back over these again; and since the next couple of lessons, we are going to be talking about segments0163
and angles, if I have, let's say, the measure of angle 1, the measure of angle 1 equals the measure of angle 2.0172
So then, if the measure of angle 1 is representing a, and the measure of angle 2 is representing b,0185
then the measure of angle 1, plus the measure of angle 3 (c is a new one) equals...what is b?...0191
the measure of angle 2, plus the measure of angle 3.0200
So, this is also the addition property of equality, but just using angles now.0204
The measure of angle 1, plus the measure of angle 3, equals the measure of angle 2, plus the measure of angle 3.0209
Then, you are adding the same angle measure to both of these sides.0214
The subtraction property is the same thing: if I have, let's say, the measure of angle 1,0220
minus the measure of angle 3, then that is the same thing as the measure of angle 2, minus the measure of angle 3.0230
The multiplication property does the same thing, and the division property would also be the same thing.0240
The reflexive property of equality: this one is when you have one number, a;0252
for every number a, then a equals ait equals itself; a = a is the reflexive property.0261
You can have a segment AB equaling itself, AB; this is also the reflexive property; measure of angle 1 = measure of angle 1reflexive property.0271
When you write this, you can write this like "reflexive"...we can write "property"...0286
and for the equality properties, even the ones that we just went over, the addition property,0296
subtraction, multiplication, and divisionsince they are all properties of equality,0301
you can write "reflexive property of," and then you can write an equals sign next to it, like that: "reflexive property," and then an equals sign.0306
And that equals sign represents the type of property that it is.0314
So, it is the reflexive property of equality.0321
The symmetric property is different than the reflexive property, because you are given two numbers,0326
a and b; you are saying that a equals something else; if a = b, then...and then, you are just going to flip it; and you say b will then equal a.0333
So, if AB = 10, then you can say 10 = AB; and that is the symmetric property.0348
For the symmetric property, you can just write "symmetric property of equality" like that, too.0361
The transitive property of equality: For all numbers a, b, and c, if a = b, and b = c, then a = c.0370
So, let's use angles: if the measure of angle 1 equals the measure of angle 2,0382
and the measure of angle 2 equals the measure of angle 3, then since this and this are the same,0390
the measure of angle 1 equals the measure of angle 3.0401
If this equals that, and that equals something else, then these two will equal each other; and that is the transitive property of equality.0404
This one you can write as "trans. property of equality" for short.0414
A couple more: the substitution property of equality: whenever you replace something in for something that is of the same value,0427
then you are using the substitution property; so if you have numbers a and b, and if a = b,0441
then a may be replaced by b in any equation or expression.0447
If I tell you that x = 4, and x + 5 = 9, then I can take this; since x is equal to 4, I see an x here;0452
so since this and this are the same, I can just replace the 4 in for x...plus 5, equals 9.0475
I am substituting in this for this; and that is the substitution property.0485
For the substitution property, be careful not to just write "sub.," because this can also be the subtraction property.0495
You can just maybe write it like that, or maybe you can write the whole thing out: "substitution property of equality."0504
The distributive property of equality: for all numbers a, b, and c, a times the sum of b and c is equal to ab + ac.0515
Remember: you take this value right here; you multiply it to all the values inside.0527
So, it is going to be a times b, and then plus a times c; and that is the distributive property.0536
You can also go the other way; you can take it from here; you can factor out the a.0548
We have an a in both terms; factor it out; in this term, I have a b, plus...and in this term, I have a c left; that is also considered the distributive property.0553
For the distributive property, you can write it like that; you can write "distributive of equality"; you can write "prop."0565
These are all properties of equality; we are going to be using them pretty often in what is called a proof.0578
And there are a couple of different types of proofs, but the main one is called the twocolumn proof.0587
And a twocolumn proof is just a way of organizing your reasoning, and it is deductive reasoning.0594
When you use twocolumn proofs, you use them to show how to come up with some kind of conclusion.0605
Remember: with deductive reasoning, we talked about having some true statements,0617
and using facts and different definitions and so on to come up with a conclusion.0623
And a twocolumn proof is just a way of organizing those things.0632
For a twocolumn proof, you are going to have a given statement, and the given statement is just whatever is given to you,0638
the information that is given; and it can be maybe the values of angles, or the values of the side measureswhatever.0652
Whatever they give you, whatever is given to you, is going to go right here, as given.0662
That is going to be given, and then they are going to give you a "prove" statement, what to prove.0668
Given this information, your conclusionhow will you get to this right here?0677
They are going to give you both statements; and then, on this side, you are going to have a diagram or some kind of drawing,0682
some kind of picture of this proofsome kind of drawing, maybe a diagram; that is going to go right here.0693
And then, right below it, you are going to have something that looks like this.0709
And it is a twocolumn proof, so you are going to have two columns.0719
On this column, you are going to have statements; on this column, you are going to have reasons.0722
You are going to state somethingyou are going to state your facts, your different things.0733
And then, on this side, you are going to have reasons for that statement.0739
You can't just say somethingyou have to have a reason; you have to back it up with something.0744
Why is that statement true? You are going to do numbers 1, 2, 3, 4...and it is going to go on.0748
And then, your reasons: 1, 2, 3, 4...you have to have a reason for every statement you write down.0756
Now, any time you do a twocolumn proof, the first statement is always going to be your given statement.0763
Whatever is written here, you are also going to write here.0772
You are going to start with your given; and then, your last statement...however many...0776
Now, you don't always have to have 4 or 5; it is usually going to be around 4, 5, or 6, but you can have less; you can have more.0784
It depends on the proof; but your last statement is going to be this statement.0793
Whatever is written here is going to be your last statement.0801
And then, for number 5, you are going to have a reason for that statement.0804
This is what a twocolumn proof looks like; now, if you are so confused by what a twocolumn proof is, think of directions.0808
From your house to, let's say, school, or from your house to a friend's house, you have a starting point.0821
You are starting at some place, and you are going to head over to school, or your friend's house, wherever it is.0833
You have directions; if you are to give someone directions to school from your houseor anywhere0843
the starting point...you have point A to point B; you have steps to get from point A to point B.0850
If you are at home, how are you going to get to point B?0860
You make a right here, make a left here, or whatever it may be; you have directions.0864
There are steps to get there; this is exactly the same thing.0869
The given statement...this is where you start; that is point Athat is your starting point; that is like your house.0874
This statement right here, the "prove" statement, is point Bthat is where you have to end up at; that is your destination.0882
You have to go from point A to point B; but again, you can't just snap your fingers and get there.0892
You have steps; you have directions to get there.0901
For each (maybe "make a right turn"; "make a left turn here"), you can't skip any steps, because it has to lead from point A,0905
and then through all of these steps, you are going to end up at point B.0916
And that is what a twocolumn proof is; they are just saying how you get from here to here.0924
And all you have to do is list out your statements: the starting point, point A, is going to be on line 1, statement 1.0928
Your last statement is going to be right here, your "prove" statement.0937
And you are just going to have reasons for that: why is this statement true? Why is this statement true?0941
Now, when you write your given statement for step 1, your reason is always going to be "Given."0946
That is the reason; this statement is true because it is giventhat is given to you.0956
So, step 1 is this part right here, the given statement; and the reason for that is "Given."0964
So, here is an example of a proof: now, here, the statements are just listed, and the reasons are just listed.0975
It is a twocolumn proof; you can draw a line out like this and draw a line down like this.0983
Or you can just do it like this; as long as you have two columns, a column for statements and a column for reasons, you still have a twocolumn proof.0992
Again, here is your given statement; you have a few things that they give you; and prove this.1002
So, look at the statements: now, for step 1 (they are not all listed out, so let me write them out here),1011
AC is 21; that is this right here; now, you have to write out all of them.1026
So then, see how only this is written out; so I am going to write in the other ones.1031
AB = 2y, and BC = 3y  9; those are all of your statements.1037
Now, here, AB is 2y; so I can write that in; so use this diagram to help you get from here, point A, to point B.1050
Write it in: AB is 2y; BC is 3y  9; and then, AC, the whole thing, is 21.1065
And, given this information, they want you to prove that y equals 6.1080
Step 1: All that I did was to copy down all of the given statements right there.1088
And the reason for that is "Given."1095
Now, the next step: AB + BC = AC...well, that is because, since I have AB, and I have BC, and I have AC,1102
AC, the whole thing, is 21; but since I need to solve for y, I need to look at where my destination is.1119
Where am I trying to get to?to what y ismy value for y.1127
Well, y, I see here, is from AB, and from BC, not from AC.1131
So, how do I mention these parts, these segments, in relation to the whole thing?1139
This is part of the segment; AB is part, and BC is another part, of this whole segment, AC.1149
If you remember, from chapter 1, we talked about segments, and then their parts.1160
I can say that AB + BC = AC; this part, plus this part, equals the whole thing: AB + BC = AC.1170
And the reason for this step, this statement, AB + BC = AC: if you remember, that is called the Segment Addition Postulate.1186
And you can just write it like this for short: the Segment Addition Postulate.1206
Now, why did I write this downwhy is this step here?1214
It is because I know that, in order for me to find the value of y, I have to look at these parts, AB and BC.1218
I can't just look at the whole thing; so when I have to look at the parts, compared to the whole thing,1227
then I have to use the Segment Addition Postulate.1233
And then, what happened here? The next step: 2y + 3y  9 = 21; so how did I get from this step to this step?1237
What happened here? Well, I know that AB is what?AB is 2y; BC is this; so, guess what happened right here.1252
You see that...and 21; AC is 21; so, since AB is 2y, just replace AB for 2y, and then replace this for this, and replace this for this.1272
Whenever you do replacing, whenever you replace something for something else, in an equation or expression, that is the substitution property of equality.1292
Now, remember: be careful not to write "sub." because that can mean subtraction; "substitution" is the shortest you can write it.1313
Or you can write the whole thing out.1323
The next step: from here, 5y  9 = 21well, how did you get from this step to this step?1327
You did this plus this; you just simplified it, and more specifically, you added; so this would be the addition property (and this is for the "equality").1340
Now, here, number 5: you did 5y, and then you added 9 to both sides; this is the addition property, because you added.1364
And then, from here, how did you get from this step to this step?1385
You divided by 5 on both sides; so this is the division property of equality.1391
And then, since we have this statement, which is the same as this statement right here, we have arrived to our destination, to point B.1406
And once you do that, then you are done; so as long as you start here and you end up here, then you are done.1416
The next example: the measure of angle CDE (there is angle CDE) and the measure of angle EDF are supplementary.1431
Prove that x = 40.1442
So, here I am going to write in...now, for this one, this is x, and this is 3x + 20.1446
Sometimes, they give you the information on the diagram; they might not always give it to you in the given.1466
The given is very important, but you have to look at the diagram, too, because they might label something1472
an angle, or give you some measure or length, and they might just write it in the diagram.1478
So, that is very, very important to have; if there is no diagram, then draw one in, because that is going to help you.1485
Especially if you are very visualif you are a visual learnerthen you should draw it in and write in whatever is given to you.1491
It will help you with your steps.1502
Number 1: Angle CDE and angle EDF are supplementary.1506
Now, to review over supplementary: supplementary means that two angles add up to 180 degrees.1514
These two angles right here, angle CDE and angle EDF, form a linear pair, meaning that,1529
when you put them together, they form a line; see how there is a line right thereso they are a linear pair.1545
And linear pairs are always supplementary, because a line measures 180 degrees.1555
So, if you have two angles that form a line, then they are supplementary.1563
If you look at supplementary angles, supplementary angles are just any two angles that add up to 180.1571
So, supplementary angles don't always form a linear pair; sometimes they do; sometimes they don't.1576
If you just have two angles that are separated, then they don't form a linear pair, but they can still be supplementary.1582
On to our proof: the reason for #1 is "Given."1591
And then, #2: I want to find x, so if I know that these two angles are supplementary, meaning that they add up to 180,1600
and then I know that these two angles together add up to 180, then I can find x that way.1614
But then, there are steps that I need to take to get there.1621
The next step is going to be that the measure of angle CDE, plus the measure of angle EDF, equals 180.1625
Now, we know that, since it says "supplementary," I can just say, "Well, since they are supplementary, then I add them together, and they equal 180 degrees."1640
And that is because of the definition of supplementary angles.1651
The definition of supplementary angles says that, if two angles are supplementary, then they add up to 180.1662
Any time you go from something supplementary to then making them add up to 180, then that would just be the definition of supplementary angles.1674
Any time you do this step, the reason will be "definition of supplementary angles."1683
The next step: now that I gave these two angles, adding them up to 180, now I have to use x somewhere, because I need to prove that x equals 40.1692
So, this angle right here became x, and then the measure of angle EDF is 3x + 20.1709
So, what happened here? Instead of writing this one, you wrote x; and instead of writing this one, you wrote 3x + 20.1722
Step #3: Since you replaced something, that is the substitution property of equality.1731
Now, #4: This right here, in the last proofthis could be the addition property, because you are adding it.1746
But it could also be the substitution property, because you are just substituting in these two for this value.1759
Let's just write "substitution property of equality."1766
And then, #5: To get from here to here, you subtracted 20 from both sides, so #5 is going to be the subtraction property.1773
And just so that you don't get confused, you can write it out, or you can just write "subtraction property," or "subtract. of equality."1798
In the next step, you divide it by 4 to get x = 40, and that is the division property, because you divided.1808
And then, we know that this is the final step, because that is what that is.1821
OK, another example: The measure of angle AXC and the measure of angle DYF...1831
oh, this is supposed to be written as "equal"; so then they are equal.1848
The measure of angle AXC and this angle are the same; and the measure of angle 1, this one, is equal to the measure of angle 3.1858
And by doing this, this is showing that they are the same.1872
So, if I do this one time, and I do this one time, that means that they are the same.1876
And I have to prove that the measure of angle 2 is equal to the measure of angle 4.1883
For this one, I don't have any statements, so we are going to have to do the statements on our own, and then come up with the reasons as we go along.1892
#1: I am going to write that the measure of angle AXC equals the measure of angle DYF,1899
and that the measure of angle 1 equals the measure of angle 3.1913
OK, and my reason for that is "Given."1925
Now, my next step: since I know that I am trying to prove this and this, that these two are equal,1932
I need to break down this big angle into its parts.1948
I know that angle AXC equals the measure of angle 1 plus the measure of angle 2.1959
So, let me write that out: the measure of angle 1, plus the measure of angle 2, equals the measure of angle AXC.1968
And the reason why I do that is because I need to somehow get that angle 2 in there somewhere.1983
And I know that these equal each other, and I know that the measure of angle 1 and the measure of angle 3 equal each other.1992
How am I going to come up with angle 2?1999
I can say that this one, plus this one, equals this big thing.2006
I am getting it in there somehow: the measure of angle 1, plus the measure of angle 2, equals the measure of angle AXC.2013
Now, I am going to do the same thing for this one, in the same step: the measure of angle 3 plus the measure of angle 4 equals the measure of angle DYF.2018
And the reason for that, if you remember from Chapter 1: this is the Angle Addition Postulate.2040
And my third step: Since all of this equals this, and all of this equals that, look at my first step right here.2060
I know that they equal each other; well, if these equal each other, doesn't that mean that all of its parts equal each other?2077
If this big angle and this big angle equal each other, then angles 1 and 2 together equal angles 3 and 4 together.2085
So, my next step is going to be: The measure of angle 1, plus the measure of angle 2,2095
equals the measure of angle 3, plus the measure of angle 4, because all of this right here equals AXC,2103
and all of this right here equals the measure of angle DYF.2114
And they equal each other; that means that all of this and all of this equal each other; so that is the only step right there.2118
Step 3: I basically just used this right here, and I substituted in the parts for that.2126
So, step 3 is going to be the substitution property; and I can put "equality."2135
Then, for #4: Now, always keep in mind what you have to prove.2146
I have to prove that this one equals this one; so I have to somehow get rid of this and this.2156
Now, look back at step 1; if you look back at step 1, see how the measure of angle 1 equals the measure of angle 3.2167
Well, here is the measure of angle 1, and here is the measure of angle 3.2177
So, since they are the same, I can use the substitution property to replace...2180
maybe measure of angle 3 for this, or measure of angle 1 for that, because they are the same.2186
I am going to just substitute in the measure of angle 1 in place of 3, since they are the same.2194
Do you see that? This is the measure of angle 1, in place of the measure of angle 3, since they are the same, since they equal each other.2209
And my reason for this one is, again, the substitution property; this property is actually used quite often.2218
And then, here, since these are the same, I can just subtract it out.2230
Then, these cancel out; I get that the measure of angle 2 equals the measure of angle 4.2238
My reason is the subtraction property of equality.2247
And I know that I am done, because this stuff is the same as that stuff.2257
Now, I know that this seems really long; but once you get used to it, and once you get more familiar with proofs,2262
they actually become kind of fun, and it is not so long; it is not so bad.2272
It is just that, since we are going over each step, and we are going over each reason, it just seems a lot longer than it is.2276
These next few examples...we are going to just go over the properties that we went over.2289
Name the property of equality that justifies each statement.2304
If 5 = 3x  4, then 3x  4 = 5: well, this one right here...remember when we had the property "if a = b, then b = a"?2309
This property is the same property as if I said that if ab = 10, then 10 = ab.2334
And this is the symmetric property of equality, meaning that it is the same on both sides; so you flip it, and it is the same.2347
The next one: If 3 times the difference of x and 3/5 equals 1, then 3x  5 = 1.2360
So, what happened herehow did you get from this to this?2371
Well, it looks like this was distributed over to everything; this became 3 times x, which is 3x; and 3 times this; 3 times 5/3...2375
this is over 1; you can crosscancel that out, and that becomes 5.2391
Then, that is how you got that 5; and minus 1; this was the distributive property of equality.2397
You can just also write "distributive...equality."2411
Name the property: Here, this is written: if 2 times the measure of angle 180...2417
no, if 2 times the measure of angle ABC equals 180 (that is how it is supposed to be written), then the measure of angle ABC equals 90.2439
OK, so if 2 times this angle is 180, then if you solve out for the measure of angle ABC, you get 90 degrees.2456
And so, how did you get from this step to that step over there?2467
Well, it looks like you divided the 2; and the measure of angle ABC equals 90; so this one was the division property of equality,2472
because you divided the 2 to get the answerdivided 2 into both sides.2487
Name the property of equality that justifies each statement.2497
For xy, xy = xy; well, this one right hereif something equals itself, this is different than the symmetric property.2501
The symmetric property is when you have something equaling something else.2511
And then, you can reverse it and say that the second thing equals the first thing.2516
In this one, there is no second thing; it is just one thing, and that one thing equals itself, so a = a; apple = apple; xy = xy.2523
Any time you have that, it is the reflexive property; "reflexive," or "reflexive property," and this is used quite often, too, in proofs.2537
If EF = GH, and GH = JK, then EF = JK.2554
Well, if 1 = 2 and 2 = 3, then 1 = 3; this is the transitive property of equality.2563
The next one: if AB + IJ = MX + IJ, then AB = MX.2585
What happened from here to get that? It looks like this happened: this is the subtraction property of equality.2595
The next one: if PQ = 5, and PQ + QR = 7, then 5 + QR = 7.2611
So, this was the equation; there is a value of PQ, and then 5 was replaced for PQ; this is the substitution property of equality.2621
Be careful when you are writing "subtraction" and "substitution."2640
It would probably be best to just write out the whole word.2644
But if you are going to write it like this, then make sure it is obvious what you are writingsubtraction property or substitution property.2648
And that is it for this lesson; we will work on some proofs for the next lesson.2660
So, we will see you next timethank you for watching Educator.com.2666
0 answers
Post by David Saver on March 12, 2015
In Example 2, for reason number 4 are you saying that the reason could be either substitution or addition property of equality?
Both answers would be correct in this situation?
Or should we write both properties down as the reason?
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Post by Khalid Khan on October 5, 2014
In Proof Example 2, wouldn't the reason for statement three be "Addition Property of Equality?" In Proof Example 1, you did 2x+(3x+9)=21, making the next step 5x9=21. You said that this was the addition property of equality. In Example 2, it would be the same reason, because you are just simplifying it, correct?
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Post by patrick guerin on September 25, 2014
what are the other types of proofs
0 answers
Post by Manfred Berger on June 1, 2013
Shouldn't the division property of equality actually only be valid for all any nonzero c?