Placeholder Image

字幕表 動画を再生する

  • 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!

  • Learn more at www.mathantics.com

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

字幕と単語

動画の操作 ここで「動画」の調整と「字幕」の表示を設定することができます

B1 中級

数学の基礎 - 角度の基礎 (Math Antics - Angle Basics)

  • 10 8
    Yassion Liu に公開 2021 年 01 月 14 日
動画の中の単語