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• Hi! Welcome to Math Antics. We're continuing our series on Geometry

• and today we're going to learn about angles.

• In our last video, we learned about points and lines,

• and that's good because we are going to need lines to make angles.

• So let's start with a couple of lines that are in the same plane.

• We're only going to be dealing with two-dimensional geometry in this video.

• These lines are conveniently called Line AB and Line CD.

• Now the important thing to notice about these two lines is that they're pointing in exactly the same direction.

• So, even if we extended them forever, they would never cross or even get closer together.

• When two lines are arranged like this, we call them 'parallel'.

• You've probably heard the term 'parallel' beforelike parallel parking, or a parallel universe,

• or parallel bars.

• Okay, so parallel lines are lines that will never cross, even if they go on forever...

• but what if I take one of our lines and give it a little nudge?

• Now the lines aren't parallel anymore. In fact, they cross at this point right here.

• Let's name it Point P.

• When lines cross at a point like this, we say that they intersect,

• and we call the point an 'intersection'.

• And when lines intersect, they form 'angles'. You can think of the angles as the spaces, or shapes,

• that are formed between the intersecting lines.

• These intersecting lines form four angles: 1, 2, 3, 4.

• But instead of calling them angle 1, 2, 3 and 4,

• in Geometry, we name them by the points used to make them.

• For example, this angle here can be called Angle DPB

• because if you trace along those points (like connect the dots) they outline that angle.

• And this angle here... we can call that Angle APD,

• because connecting those dots forms angle.

• Now when naming angles, there's a nice shorthand we can use.

• Instead of writing the word 'angle' over and over again,

• we can just use the angle symbol instead, which looks like this.

• But there's an even simpler way to name angles.

• To learn that way, let's erase all the points and letters on our lines

• except for the intersection point and this one point here.

• Now let's imagine that the line-segment between these two points can rotate around the point of intersection,

• just like a clock hand rotates around the center of a clock.

• Let's also imagine that as we rotate the line segment,

• the point out at the end leaves a trail, like if a pencil was attached to it.

• The trail (or path) that is left when we rotate the line-segment all the way around forms a circle.

• But if we only go part way around, then it forms part of a circle that we call an 'arc'.

• This arc can represent the angle that is formed when we rotate the segment

• from one position to another, like from this line to that line.

• And now, if we shrink down that arc so that it's close to the intersection point,

• and then put a letter by it, like the letter 'A', we have another way of showing an angle...

• Angle A.

• And we can do this with any angle, so the angle up here...

• we can also draw an arc and call it Angle B.

• So whenever you see a letter next to a little arc like this,

• it means that it's the name of the angle formed by that arc.

• Alright then, so now we have a diagram that shows Angle A and Angle B,

• and you might notice that those angles aren't the same size.

• B seems to be bigger than A.

• But what if we rotate one of our lines until the angles do look like they're the same size?

• Now our angles look kind of like a plus sign. Lines arranged like this are called 'perpendicular'.

• Perpendicular lines are lines that form square corners when they intersect.

• And these square corner angles have a special name in Geometry because they are really important.

• We call them 'right angles'.

• There is even a special symbol that we use to show when an angle is a right angle.

• Because they form square corners,

• we use a little square instead of the arc that we use for the other angles.

• So whenever you see this symbol, you know the angle you are looking at is a right angle,

• and that the lines that form it are perpendicular.

• Okay, now that you know what a right angle is, let's look at a simple one that's made from just two rays.

• What will happen if we take the ray pointing up and rotate it like the hand of a clock

• a little to the right… a little bit clockwise?

• Well, we don't have a right angle any more because the rays are no longer perpendicular.

• Instead, we have an angle that is smaller (or less) than a right angle.

• Angles that are less than right angles are called 'acute angles'.

• On the other hand, if we rotated our ray to the left instead of the right,

• we would get an angle that's bigger or greater than a right angle.

• Angles that are greater than right angles are called 'obtuse angles'.

• So, there are three main kinds of angles that you need to know about.

• Right Angles, acute angles and obtuse angles.

• Well actually, there's one more type of angle that's pretty important,

• but it's kind of a strange one. It's called a 'straight angle'.

• A straight angle is just what we get when we rotate our rays so that they point in exactly opposite directions.

• The result looks just like a straight line, which is why it's called a straight angle.

• Alright then, there's just a few more important geometry terms that we need to learn in this video.

• Let's look at our simple right angle again that's made from two rays.

• But this time, let's draw a third ray that cuts that right angle into two smaller parts.

• Now, because the angle that we divided up was a right angle,

• we know that the two new smaller angles combine to form a right angle.

• And in geometry, any two angles that to form a right angle are called 'complementary angles'.

• And we can do the same thing with a straight angle.

• If we take a straight angle (made from two rays)

• and divide it with a third ray, two new smaller angles are formed.

• And those two angles combine to form a straight angle. We call these angles 'supplementary angles'.

• So, complementary angles combine to form a right angle,

• and supplementary angles combine to form a straight angle.

• Alright, that's all were going to learn about angles in this video.

• And if you are new to Geometry, it might seem like a lot,

• so let's do a quick review of all the new geometry words we've learned.

• Lines that point in exactly the same direction will never cross and are called 'parallel' lines.

• When lines do cross, they cross at a point called an 'intersection'.

• Lines that intersect form 'angles'. You can think of angles as the spaces between the lines.

• Angles can be named by the points that form them... just like connect the dots.

• An 'arc' is a part of a circle. Arcs can be used to represent an angle between two intersecting lines.

• When intersecting lines form all exactly equal angles, the lines are 'perpendicular'.

• Perpendicular lines form 'right angles'. Right angles are square corners,

• and we use a special square symbol to show that an angle is a right angle.

• An angle that's smaller, or less than a right angle is called an 'acute angle'.

• An angle that's bigger, or greater than a right angle is called an 'obtuse angle'.

• A 'straight angle' is formed by two rays pointing in exactly opposite directions.

• A straight angle is really just a straight line.

• Two angles that combine to form a right angle are called 'complementary angles'.

• Two angles that combine to form a straight angle are called 'supplementary angles'.

• In our next geometry video, we're going to learn more about angles and how to measure them.

• Thanks for watching Math Antics, and I'll see you next time!