# Parallel Lines & Transversal Angles

I somehow need to…you know, I could match 6 to 2, I could go through the angle of 4…I could go through the angle of 3, which is how we are going to approach this proof. And regardless of whether you want to show a relationship between… or you could go through 5…I want to go with the 1 and 3. Now, if I have angle 1 and angle 3, and I cover up the rest of the diagram that is not specifically related to those two angles, I see that angles 1 and 3 are adjacent and forming a straight line. Which means that angle 1 and 3 are a linear pair.
And that means that not only 1 and 3 are going to be a linear pair, but what does that mean?
Linear pairs are supplementary. By definition. Let’s get that written for step number 2. Well, you might want to say linear pairs are supplementary. Maybe your teacher is happy with just definition of linear pair. Maybe they are just happy if you write linear pair. Talk to your teacher about what they want. If angle 1 and 3 are supplementary, what does that mean? Supplementary angles are two angles that add up to 180 degrees. Let’s get that written out. So perfect example of when you build a proof…I am already out of sequence from what I wrote in my notes. When you build a proof, all that is important is… you know, if I want to make a statement in line 6, it is probably going to need to be using information that I built on in the previous statements. Some statements you can make at any point and it is perfectly fine. And other statements you need to pull from facts that you have justified earlier in the proof.
At this point, I have made some statements and I didn’t need to pull on any kind of knowledge or statements that have been made earlier in the proof. At this point, I am just stating facts. I have not really seen a connection or string of information that I need to put together. I am just writing stuff down that I figured out. So I have a relationship between 1 and 3.
Now that I have some kind of relationship between 1 and 3, we might not know really where it is going yet…If I am making statements about 3, we do know how 3 is related to 6.
Ultimately, we want to prove something about 1 and 6. That they are supplementary. So I need to string those angles together through some other angle. And that now is going to be 3, because I have introduced it into my proof. In lines 2 and 3. We are going to say that angles 3 and 6 are congruent. And they are, because they are alternate interior angles. And when parallel lines are cut by a transversal, the alternate interior angles are congruent. And I do not want to talk about 4 and 5 because they have nothing to do with ultimately what we want to prove. So I am going to step out and say that angle 3 is congruent to angle 6. So alternate interior angles of parallel lines are congruent. And that means that angle 3 is congruent to angle 6. But ultimately, I’ve got this equation up here that has a statement about measures. And I do not have anything about measures of 3 and 6 together, so just a small step… but what are congruent angles? Angles that have equal measure. Now we are that the point where the next line is going to have to build on information that I have justified and stated earlier in my proof.
And if I look here, I’ve got the measure of angle 1 plus the measure of angle 3 equals 180. Again, the proof is about angles 1 and 6 being supplementary or 1 and 6 adding up to 180. But down here, I have justified now that the measure of angle 3 is equal to the measure of angle 6. So, I have take my 3 – the measure of angle 3, that symbol or notation that is in this equation… take it out and plug in what it is equal to. Which is 6.
Do you see what is happening? I am going to have one equation saying that with substitution, taking the 3 out and plugging in the measure of angle 6…I am going to have a statement that says the measure of angle 1 plug the measure of angle 6 is equal to 180.
And that means I am almost done with my proof! Very cool! Well… This is not what I am trying to prove. This does not say EXACTLY the same thing. This says the measure of angle 1 plus the measure of angle 6 is equal to 180. And I am trying to prove that they are supplementary. But…isn’t that kind of the same thing?
It’s not formally in the proof yet, in my sequence of logic, but it is what is coming up next.
We are just going to say that the measure of angle 1 and 6 are supplementary because that is the definition of supplementary. Whoo! BAM! There we go! Proof is done! Again, as we go through geometry, some people will get these proofs like boom, boom, boom! And some people are going to struggle with them. Maybe just always struggle with them. You need to make sure that you know your defintions, you postulates, your theorems right off the top of your head.
Make an organized…some kind of notes where the properties are on one side and what they say are on the other. And you can fold it and know them back and forth. Or flash cards… something where you know those statements right off the top of your head. And as we do these examples, I am going to build these proofs from scratch and hopefully help you see the logic string… you know, we have a complex problem, but there were at least a few steps to get from point A to point B.
The real point of proofs is to help you develop those logical thinking skills of, “hey! I’ve got this complex problem, how can I work it out and find a good, logical sequence of steps that will allow me to complete the problem or solve the issue?” You do not get that in a lot of classes. However, I do see a lot more with the newer books…they give you these proofs, and it is just like You are not given the reason, or you are given the reason and not the statement. That is more, unfortunately, just a memorization type problem. It does not strengthen your logic building skills. They are good examples, and you should pay attention to how the facts are stringed together, to strengthen your own logical problem-solving skills.
That is really what you need to take out of these kinds of problems, once you are out of geometry. I’m Mr. Tarrou! BAM! Go do your homework!

• ProfRobBob says:

Angles X & Y were not a linear pair…though I did erase part of the diagram to help explain how to find the value of X which equals 60 degrees. The third angle of the triangle would be 59 degrees if we had found it and 59+60+61=180. Your question did point out to me…that I apparently lost one of the clips that I shot for this video:(

• mico kolo says:

hi there im thanking you because it helped me to make a lesson in class its kinda embarrass me cuz they are my fellow classmate anda graded recitation in math bbut your vid teach me a lot thank you

• mico kolo says:

tnx for your vid it help me a lot and was able to complete my lessons for my fellow classmate

• ProfRobBob says:

You're welcome…I'm happy to hear that it helped you to complete your lesson for your classmate:)

• Glen Johnson Ironman says:

That was good, I had to replay the end explanation of the reasoning for learning and making more concrete (in teaching terms) the logical sequences for proofs as I was reading your shirt- which I like alot Mr. T. Thanks, great vid!

• Eisa Sheikh says:

At maths class the teacher put your video up

• Eisa Sheikh says:

At maths our teacher put your video up for us

• XxXLi_pokemonXxX XxX says:

I'm so glad i found this channel. The teacher at our school doesn't teach. And when he does teach, he does it too fast, and no one understands. I wish you were my teacher. Is there any tricks to remember this? I have a test tomorrow and i don't think ill do good on this.

• FromHere2Where says:

Where can I order a T-shirt like yours?

• sam cx says:

Im gonna fail my quiz great

• Karla Rivas says:

I was having trouble with finding parallel and perpendicular lines equations and when I saw ur video on the topic of parallel and perpendicular lines I got a C+ on my test and this had improved from an F I was so happy. Thank You ProfRobBob.

• YAHOO says:

Hi. i have a question about #2 example, why can't Y be equals to 121deg, since there are 2 given angle measurements in the triangle and we know that it is equals to 180deg, then the third angle measures 59 deg. 60+61+59=180. 59 is supplementary to Y so Y will be equals to 121deg? But the figure is an acute angle. I'm really confuse. pls explain thank you.

• Samir Dawud says:

I appreciate the hard work for this vid thanks

• Kashak Attry says:

You should explain more nicely I can't understand what you are teaching and pls don't show your face while teaching.😊

• shaune Robinson says:

don't know how to do it

• Fortnite gamer LUU says:

What

• Shaafimath says:

Thanks alot! but Example 2 seems to me wrong! why ? because you got X=60 and Y = 61 . when we look at another way angle X and Y are supplementary angle and they must be add up 180. so why the solution of the two ways must be the same ???

• aja franklin says:

I can hear him clearly and see what he's doing, but I wish the screen was bigger; closer to the board I mean.

• Naavya Sheth says: