Math Antics - Quadrilaterals - Free Educational videos for Students in K-12

Math Antics - Quadrilaterals - By Mathantics

Transcript


00:03	Uh huh . Hi , welcome to Mathematics . In
00:08	this video , we're going to learn about special kinds
00:10	of polygons called quadra laterals . Quadrilateral is just a
00:15	fancy math word for a polygon that has exactly four
00:18	sides and four angles like this one . You should
00:21	recognize this shape . Of course it's a square and
00:24	a square is a special kind of quadrilateral . It's
00:28	a quadrilateral because it has four sides and it's special
00:31	because all four of those sides are exactly the same
00:34	length and all four of its angles are exactly the
00:37	same size . In fact , they're all right angles
00:41	. Notice also that a square is formed by two
00:44	pairs of parallel sites . These two opposite sides are
00:47	parallel and these two opposite sides are parallel . We'll
00:50	see why that's important in a few minutes . Okay
00:54	, so squares are an important type of quadrilateral but
00:57	we're going to make some changes to the square to
00:59	see what other types of quadrilateral . There are the
01:02	two things that we can change our the sides and
01:05	the angles . Let's start by changing the sides .
01:08	Let's stretch our square in one direction so that one
01:12	pair of sides is now longer than the other pair
01:14	. This is what we call a rectangle . A
01:18	rectangle is a quadrilateral that still has four equal angles
01:22	. Noticed that when we stretch the square , the
01:24	angles didn't change at all , But it does not
01:27	have four equal sites . Again notice it just like
01:31	a square . A rectangle is made from two pairs
01:34	of parallel sides . All right , So that's a
01:37	rectangle . But going back to our square . What
01:40	if instead of changing the sides , we had just
01:42	changed the angles like this . Ah What we have
01:46	now is called a rhombus . A rhombus is a
01:49	quadrilateral that still has four equal sides , but it
01:53	does not have four equal angles . And once again
01:56	, just like the square and rectangle , the rhombus
01:59	is made from two pairs of parallel sides . Okay
02:04	, going back once more to our square . What
02:07	if we try changing both the sides and the angles
02:10	? Here's what we end up with . And we
02:12	call it a parallelogram . It's called a parallelogram because
02:17	even though it's sides are not all equal and its
02:19	angles are not all equal , it's still made from
02:22	two pairs of parallel sites . Get it parallel parallelogram
02:27	. Now wait a second . If that's the definition
02:30	of the parallelogram , a quadrilateral that's made from two
02:33	pairs of parallel sides then one in all these other
02:36	shapes be parallelogram is too Exactly . All of these
02:42	shapes are parallel in grams , just like they're all
02:44	quadra laterals . It's just that we have special names
02:47	for them . If they're angles are all equal a
02:50	rectangle or if their sides are all equal a rhombus
02:53	or if both their sides and their angles are all
02:57	equal a square . Okay then if all the quadra
03:01	laterals we've seen so far are examples of parallelogram .
03:05	What's an example ? That's not a parallelogram ? Well
03:08	to see one let's start over with our square again
03:11	. But this time we're going to change it by
03:13	moving just one of its vertex is like , so
03:17	now one of the pairs of science is still parallel
03:20	but the other is not . And a quadrilateral that
03:23	has only one pair of parallel sides is called a
03:27	trapezoid . Well actually this is where classifying quadra laterals
03:32	gets a little messy and that's because this sort of
03:35	shape is called a trapezoid in America but it's called
03:38	the Trip Easy . Um In other countries like the
03:40	UK trapezoid Trip Easy um trap is oid trapezius .
03:48	It's a trapezoid . No . Uh huh . At
03:53	least they both start with the word trap so it's
03:56	not too confusing yet . Okay so this quadrilateral is
04:01	a trapezoid or Trip easy um because it has only
04:04	one pair of parallel sites and the other sides are
04:08	not parallel . Here are a couple more examples of
04:11	quadra laterals that have only one set of parallel sides
04:16	. All right then . What about quadra laterals that
04:19	have no parallel sides at all ? Like this one
04:22	these opposite sides are not parallel and these opposite sides
04:25	are parallel either . So what do we call this
04:27	kind of polygon ? Now here's a really confusing part
04:32	in America . This is sometimes called a Trip Easy
04:34	. Um But isn't that what they call a quadrilateral
04:37	with only one pair of parallel sides in the UK
04:40	, yep . Unfortunately the same word is used to
04:44	describe two different things in two different countries , trapeze
04:49	ium trapeze , iem trapeze Iem Trip Easy . Um
04:55	trapezes , trapeze ium Well at least they both like
05:00	football but to keep things clear at math . Antics
05:04	were not going to call a quadrilateral that has no
05:06	parallel sides a trip Easy . Um We don't think
05:08	it needs a special name , so we're just going
05:10	to call it a quadrilateral . So to summarize any
05:14	polygon that has exactly four sides is called a quadrilateral
05:19	and if it has no parallel sides , we still
05:22	just call it a quadrilateral . But if it has
05:25	one and only one pair of parallel sides , we
05:28	call it a trapezoid or a trip easy . Um
05:31	or if it has two pairs of parallel sides ,
05:34	we call it a parallelogram . And you've already seen
05:37	that there are several types of parallelogram called rectangles ,
05:41	rhombus is and squares . All right , so that's
05:45	the basics of classifying quadra laterals and there's a few
05:48	other special types of quadra laterals but we've learned the
05:51	most important ones But there is one more really important
05:55	thing you need to know about quadra laterals . You
05:57	need to know that the sum of the angles of
05:59	a quadrilateral is always 360°. . Now that's pretty obvious
06:05	for a square or a rectangle . Those shapes have
06:08	four right angles and since we know that a right
06:11	angle is 90°4 times 90 gives us 360 . But
06:16	to see that it's also true for any quadrilateral ,
06:19	let's have a look at these four different examples .
06:22	Watch what happens when we draw a line on each
06:25	of them between a pair of opposite vertex ? Is
06:28	each of the quadra laterals got divided into two triangles
06:33	In the triangles . Video we learned that the sum
06:35	of the angles of a triangle is always 180°. .
06:39	So it's not too hard to see that since the
06:42	angles of a quadrilateral formed two triangles , the some
06:45	of those angles would be two times 180°, , which
06:49	is 360 . Knowing that the angles of a quadrilateral
06:54	add up to 360 degrees . Can help you solve
06:57	problems like this one for this quadrilateral . We're told
07:00	what three of the angles are , but the fourth
07:02	one is unknown To find the unknown angle . All
07:06	we have to do is add up the three angles
07:08	that we do know and then we subtract that from
07:11	the total , which we now know is 360°. .
07:15	So 100 plus 80 plus 60 equals 240 And then
07:22	360 -240 equals 120 . So the unknown angle is
07:29	120°. . Let's look at one more unknown angle problem
07:35	. That's a little tricky . This problem asked us
07:38	to find the unknown angle A . In a parallelogram
07:41	but it looks like they only told us what one
07:44	of the angles is and the other three are unknown
07:46	. So how can we possibly figure this one out
07:50	to solve this problem ? We need to know an
07:52	important fact about parallelogram because parallelogram are always made from
07:57	pairs of parallel sides . That means they also form
08:01	pairs of equal angles . It's the opposite angles that
08:04	form these pairs . For example , in this parallelogram
08:09	, the angles A and C . Are equal because
08:12	they're on opposite corners and the angles B and D
08:15	are equal because they're on opposite corners . Now ,
08:18	remember this is only true for parallelogram . This won't
08:22	work for things like trapezoid size . So in our
08:25	problem , even though we're only given the measure of
08:27	one angle , since we know it's a parallelogram ,
08:30	that's all . We need to figure out all the
08:32	other angles . First of all , we know that
08:35	angle B must also be 50° because these opposite angles
08:39	must be equal . Next we know that the other
08:43	two angles A and C must also be equal .
08:46	So if we can figure out how many degrees are
08:49	left over or still unknown , we can just divide
08:52	that amount equally between A . And C . Well
08:56	the total of all the angles is 360 . So
09:00	if we subtract the angles that we know 50 plus
09:03	50 equals 103 160 minus 100 equals 260 . We
09:09	know that a . And c . must each behalf
09:12	of 260° And 260 divided by two is 130 .
09:19	So angle a must be 130°. . Okay , that's
09:25	all for this video . We've learned the basics of
09:27	how to classify quadra laterals and we learned that a
09:31	quadrilateral angles add up to 360°. . Remember getting good
09:36	at math takes practice . So be sure to work
09:39	the exercises for this section as always . Thanks for
09:42	watching Math Antics and I'll see you next time .
09:45	Learn more at Math antics dot com .

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