Math Antics - Angle Basics - Free Educational videos for Students in K-12

Math Antics - Angle Basics - By mathantics

Transcript


00:03	Uh huh . Hi , welcome to Math Antics .
00:08	We're continuing our series on geometry and today we're gonna
00:11	learn about angles . In our last video , we
00:14	learned about points and lines and that's good because we're
00:17	gonna need lines to make angles . So let's start
00:19	with a couple of lines that are in the same
00:21	plane . We're only going to be dealing with two
00:23	dimensional geometry in this video . These lines are conveniently
00:26	called Line A . B . And line C .
00:29	D . Now the important thing to notice about these
00:32	two lines is that they're pointing in exactly the same
00:34	direction . So even if we extend them forever ,
00:37	they would never cross or even get closer together When
00:41	two lines are arranged like this , we call them
00:43	parallel . Now . You've probably heard the term parallel
00:45	before . Like parallel parking or a parallel universe or
00:48	parallel bars . Okay , so parallel lines are lines
00:59	that will never cross even if they go on forever
01:02	. But what if I take one of our lines
01:03	and give it a little nudge ? Now the lines
01:06	aren't parallel anymore . In fact they cross at this
01:09	point right here let's name it point P . When
01:12	lines cross at a point like this we say that
01:14	they intersect and we call the point an intersection .
01:17	And when lines intersect they form angles , you can
01:20	think of the angles as the spaces or shapes that
01:23	are formed between the intersecting lines . These intersecting lines
01:26	form four angles 1234 But instead of calling them and
01:32	go 123 and four . In geometry , we named
01:35	them by the points used to make them . For
01:37	example this angle here can be called angle DPB because
01:41	if you trace along those points like connect the dots
01:44	, they outline that angle . And this angle here
01:47	we can call that angle A . P . D
01:49	. Because connecting those dots forms that angle . Now
01:53	, when naming angles , there's a nice shorthand that
01:55	we can use instead of writing the word angle over
01:57	and over again we can just use the angle symbol
02:00	instead which looks like this . But there's an even
02:03	simpler way to name angles to learn that way .
02:06	Let's erase all the points and letters on our lines
02:08	except for the intersection point and this one point here
02:12	. Now let's imagine that the line segment between these
02:15	two points can rotate around the point of intersection just
02:18	like a clock . Hand rotates around the center of
02:20	a clock . Let's also imagine that as we rotate
02:24	the line segment , the point out at the end
02:26	leaves a trail like if a pencil was attached to
02:29	it , the trail or path that's left . When
02:32	we rotate the line segment all the way around forms
02:35	a circle . But if we only go part way
02:37	around then it forms part of the circle that we
02:40	call an arc . This arc can represent the angle
02:43	that's formed when we rotate the segment from one position
02:46	to another , like from this line to that line
02:49	. And now if we shrink down that arc so
02:51	that it's close to the intersection point and then put
02:54	a letter by it like the letter A . We
02:56	have another way of showing an angle angle A .
02:59	And we can do this with any angle . So
03:02	the angle up here , we can also draw an
03:04	arc and call it angle be . So whenever you
03:07	see a letter next to a little arc like this
03:10	, it means that it's the name of the angle
03:12	formed by that arc . All right then . So
03:15	now we have a diagram that shows angle A .
03:17	And angle be . And you might notice that those
03:20	angles aren't the same size B . Seems to be
03:23	bigger than a . But what if we rotate one
03:26	of our lines until the angles do look like they're
03:28	the same size ? Now our angles look kind of
03:31	like a plus sign lines arranged like this are called
03:34	perpendicular , perpendicular lines are lines that form square corners
03:39	when they intersect . And the square corner angles have
03:42	a special name in geometry because they're really important .
03:45	We call them right angles . There's even a special
03:48	symbol that we use to show when it angles are
03:50	right angle because they form square corners . We use
03:53	a little square instead of the ark that we use
03:56	for the other angles . So whenever you see this
03:58	symbol , you know that the angle you're looking at
04:01	is a right angle and that the lines that form
04:04	it are perpendicular . Okay , now that you know
04:07	what a right angle is , Let's look at a
04:09	simple one that's made from just to raise . What
04:12	will happen if we take the rape pointing up and
04:15	rotate it like the hand of a clock , a
04:17	little bit to the right , a little bit clockwise
04:19	. Well we don't have a right angle anymore because
04:22	the rays are no longer perpendicular . Instead we have
04:26	an angle that smaller or less than a right angle
04:29	angles that are less than right angles are called acute
04:32	angles . On the other hand , if we rotated
04:35	our right to the left instead of the right ,
04:37	we would get an angle that's bigger or greater than
04:40	a right angle angles that are greater than right angles
04:43	are called obtuse angles . So there are three main
04:47	kinds of angles that you need to know about right
04:49	angles , acute angles and obtuse angles . Well actually
04:53	there's one more type of angle that's pretty important but
04:56	it's kind of a strange one . It's called a
04:58	straight angle . A straight angle is just what we
05:02	get when we rotate our raise so that they point
05:04	in exactly opposite directions . The result looks just like
05:08	a straight line , which is why it's called a
05:10	straight angle . All right , then there's just a
05:13	few more important geometry terms that we need to learn
05:16	in this video . Let's look at our simple right
05:18	angle again , that's made from to raise . But
05:21	this time let's draw a third ray that cuts that
05:24	right angle into two smaller parts . Now because the
05:27	angle that we divided up was a right angle ,
05:30	we know that the two smaller angles combined to form
05:32	a right angle . And in geometry any two angles
05:36	that combined to form a right angle are called complementary
05:39	angles . And we can do the same thing with
05:42	a straight angle if we take a straight angle made
05:45	from to raise and divide it with a third ray
05:48	to new , smaller angles are formed and those two
05:51	angles combined to form a straight angle , we call
05:54	these angles supplementary angles . So complementary angles combined to
05:59	form a right angle and supplementary angles combined to form
06:03	a straight angle . All right , that's all we're
06:06	going to learn about angles in this video and if
06:08	you're new to geometry , it might seem like a
06:10	lot . So let's do a quick review of all
06:13	the new geometry words . We've learned lines that point
06:17	in exactly the same direction will never cross and are
06:20	called parallel lines . When lions do cross , they
06:24	cross at a point called an intersection lines that intersect
06:28	form angles . You can think of angles as the
06:31	spaces between the lines , angles can be named by
06:34	the points that form them just like connect the dots
06:38	. Mhm An arc is a part of the circle
06:41	. Arcs can be used to represent an angle between
06:44	two intersecting lines when intersecting lines form all exactly equal
06:49	angles . The lines are perpendicular , perpendicular lines form
06:54	right angles . Right angles are square corners , and
06:58	we use a special square symbol to show that an
07:01	angle is a right angle . An angle that smaller
07:04	or less than a right angle is called an acute
07:07	angle . An angle that's bigger or greater than a
07:10	right angle is called in a to strangle . A
07:13	straight angle is formed by to raise , pointing in
07:16	exactly opposite directions . A straight angle is really just
07:20	a straight line . A 22 angles that combined to
07:24	form a right angle are called complementary angles . Two
07:28	angles that combined to form a straight angle are called
07:31	supplementary angles . In our next geometry video , we're
07:36	going to learn more about angles and how to measure
07:38	them . Thanks for watching Math Antics , and I'll
07:40	see you next time learn more at Math Antics dot
07:44	com .

Summarizer

DESCRIPTION:

OVERVIEW:

Math Antics - Angle Basics is a free educational video by mathantics.

This page not only allows students and teachers view Math Antics - Angle Basics videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.