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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