Angle relationships example (video) | Angles | Khan Academy
It's all a matter of degrees! In this BrainPOP movie, Tim and Moby introduce you to the concept of angles and how to measure them. You'll learn what makes an. In this lesson, you'll learn to prove angle relationships using properties of congruent, complementary, and supplementary angles. Learn the. Learn about angle relationships with Flocabulary's educational hip-hop song and lesson resources.
So it would be this angle right over here. Actually, what we already highlighted in magenta right over here. So this is angle DGB. Which could also be called angle BGD.Angle Relationships
These are obviously both referring to this angle up here. Name an angle that forms a linear pair with the angle DFG.
So we'll put this in a new color. Sorry, DGF, all of these should have G in the middle. So linear pair with angle DGF, so that's this angle right over here. So an angle that forms a linear pair will be an angle that is adjacent, where the two outer rays combined will form a line.
So for example, if you combine angle DGF, which is this angle, and angle DGC, then their two outer rays form this entire line right over here. So we could say angle DGC. Or, if you look at angle DFG, you could form a line this way. If you take angle AGF, so if you take this one, then the outer rays will form this line. So angle AGF would also work. Let's do one more. Name a vertical angle to angle FGB.
So this is FGB right over here. You could imagine this angle is one of the four angles formed when CF-- let me highlight this, that's hard to see.
Angles, parallel lines, & transversals (video) | Khan Academy
This is the last one, so I can make a mess out of this. That angle is formed when CF and EB intersect with each other. And let's say that these lines both sit on the same plane. And in this case, the plane is our screen, or this little piece of paper that we're looking at right over here. And they never intersect. So they're on the same plane, but they never intersect each other.
If those two things are true, and when they're not the same line, they never intersect and they can be on the same plane, then we say that these lines are parallel. They're moving in the same general direction, in fact, the exact same general direction. If we were looking at it from an algebraic point of view, we would say that they have the same slope, but they have different y-intercepts.
Angles - BrainPOP
They involve different points. If we drew our coordinate axes here, they would intersect that at a different point, but they would have the same exact slope. And what I want to do is think about how angles relate to parallel lines. So right over here, we have these two parallel lines.
We can say that line AB is parallel to line CD. Sometimes you'll see it specified on geometric drawings like this. They'll put a little arrow here to show that these two lines are parallel. And if you've already used the single arrow, they might put a double arrow to show that this line is parallel to that line right over there.
Now with that out of the way, what I want to do is draw a line that intersects both of these parallel lines.
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So here's a line that intersects both of them. Let me draw a little bit neater than that. So let me draw that line right over there. Well, actually, I'll do some points over here. Well, I'll just call that line l. And this line that intersects both of these parallel lines, we call that a transversal. This is a transversal line. It is transversing both of these parallel lines.
Angle relationships example
This is a transversal. And what I want to think about is the angles that are formed, and how they relate to each other. The angles that are formed at the intersection between this transversal line and the two parallel lines. So we could, first of all, start off with this angle right over here.
And we could call that angle-- well, if we made some labels here, that would be D, this point, and then something else. But I'll just call it this angle right over here.
We know that that's going to be equal to its vertical angles. So this angle is vertical with that one. So it's going to be equal to that angle right over there. We also know that this angle, right over here, is going to be equal to its vertical angle, or the angle that is opposite the intersection.
So it's going to be equal to that. And sometimes you'll see it specified like this, where you'll see a double angle mark like that.
Or sometimes you'll see someone write this to show that these two are equal and these two are equal right over here. Now the other thing we know is we could do the exact same exercise up here, that these two are going to be equal to each other and these two are going to be equal to each other.
They're all vertical angles. What's interesting here is thinking about the relationship between that angle right over there, and this angle right up over here. And if you just look at it, it is actually obvious what that relationship is-- that they are going to be the same exact angle, that if you put a protractor here and measured it, you would get the exact same measure up here.
And if I drew parallel lines-- maybe I'll draw it straight left and right, it might be a little bit more obvious. So if I assume that these two lines are parallel, and I have a transversal here, what I'm saying is that this angle is going to be the exact same measure as that angle there.
And to visualize that, just imagine tilting this line. And as you take different-- so it looks like it's the case over there.