# HK3 POLYGONS

This eighth grade mathematics lesson focuses on deriving the sum of the interior angles of a polygon. It is the first session in a sequence of four lessons working towards the more advanced concepts of polygons. The lesson is taught in English and is 34 minutes in duration. There are 41 students in the class.

TimeCaption
00:00:03Good morning, class.
00:00:04E:00]
00:00:07Okay.
00:00:15Hello, hello, hello. [ In Chinese ]
00:00:17Okay uh, boys and girls uh, for today, we are going to discuss a topic, okay? Uh... polygon.
00:00:28Polygon. Okay? Uh, for last Friday, I have asked you to prepare for this topic, have you read over this chapter?
00:00:37Yes.
00:00:38Yes, okay. Uh, I try to ask some- someone to tell me what- what you have, uh, read over for the, uh- last weekend.
00:00:47Okay, close all your textbook.
00:00:52Okay, uh, first of all, you know what- what I am now going to do?
00:00:56Okay, try to draw some diagram, what you have read from, uh, one point, uh, four. Okay? Thirty-three. Yeah.
00:01:19Okay, very good.
00:01:21Uh, this kind of the, uh, polygon we call a con- a convex polygon, okay?
00:01:29It is, we have one, two, three, four, five, six, we call it a convex hexagon.
00:01:38I use the number to present that it is six-sided. The polygon is six-sided. Okay.
00:01:44And I want another boy or girl to come up to draw another type of... polygon. Okay, another type.
00:01:56Seventeen. Seventeen? Okay.
00:02:03You draw the diagrams only. Yes. Ha ha.
00:02:09You- you- you- you draw it here, okay. I- I- I- I- I want you to draw an- another type of polygon.
00:02:22Uh, okay, thank you. For- uh, how many sides?
00:02:27Five.
00:02:28Five sides, it is, we call...?
00:02:31Do- do you know the name of this, uh, polygon? You forget it? Okay, it is a pentagon. It is a pentagon.
00:02:38I- I want you to draw another type of polygon- another property. Okay?
00:02:44Uh, for- for these two types, they are the same. We- we call them convex. Okay, convex.
00:02:49I- I- I want you to draw another type, do you know another type? I- I don't know whether you- you know or not.
00:02:56Uh, another one. Thirty-five. Who's 35? Yeah.
00:03:04You try.
00:03:16An- an- anyone you like.
00:03:25Okay, okay, thank you. Uh, do you find that such kind of a polygon is different from these two?
00:03:35Okay? We call this one... a concave polygon. Concave.
00:03:42And at the same time, how many sides for this polygon? One, two, three, four, five. Do you still remember what to call this kind of polygon?
00:03:54You have five sides, you- pentagon. How to spell pentagon? P-E-N-T-A-G-O-N.
00:03:59P-E-N-T-A-G-O-N.
00:04:04Okay, we read it together. Pentagon.
00:04:06E:00]
00:04:07Okay. I- do you find that... uh, for this one we call that convex- convex polygon, this type we call concave polygon.
00:04:16Do you find that- what is the characteristic between them? What is the difference between them?
00:04:23Okay? I'll give you, uh- uh- one minute to discuss with your neighbor. Okay?
00:04:27Can you tell me the difference between these two kind of polygons?
00:04:48Can you tell me the difference between them?
00:04:56Okay.
00:05:00Anybody try to tell me the difference between them?
00:05:06Anybody? Anybody try?
00:05:10Okay. Twenty-six. Who is 26?
00:05:19Yes. Uh, you can come out and draw anything you like to- to tell me your- your- your result. Yes.
00:05:26(inaudible)
00:05:27What is the difference between the convex polygon and concave polygon? Yes. Come up here- yes.
00:05:39Huh? What does it mean?
00:05:46Yes, okay.
00:05:48(inaudible)
00:05:50Uh, your neighbor. You- you should help him because you discussed it together. Can you come out?
00:06:00What- what- what? Yes, yes.
00:06:07What- what does it mean? What does it mean?
00:06:13Uh, more than 180 degrees.
00:06:16More- more than 180 degrees?
00:06:19Yes.
00:06:20Okay, that means- uh, this angle is more than 180 degrees?
00:06:23Yes.
00:06:24How- how about this polygon?
00:06:28Can we find any angles more than 180 degrees?
00:06:31No.
00:06:32No. Okay, can- can you get the meaning of- of- of your- thank you, thank you, your- your classmate say?
00:06:40Yeah.
00:06:41Okay, what are the differences between convex polygon and concave polygon?
00:06:45We look at the concave polygon. At least- at least one or more of the interior angles is greater than 180 degrees.
00:06:56We call this concave polygon. Understand?
00:06:59But in this chapter, we don't discuss the concave polygon, we just only discuss the convex polygon. Okay?
00:07:06Another thing, you have learned in Form One. You have learned in Form One, these two words.
00:07:15Sorry. It is uh, uh, you have learned it in Form One. It is the... equilateral polygon and also... equiangular polygon.
00:07:32What are they? What is meant by equiangular polygon? And what is meant by equilateral polygon?
00:07:41Okay, first of all, do you still remember equiangular polygon? What is meant by equiangular polygon?
00:07:50That means- okay, I- I- I- I- I- give you some time to think. What does it mean by equilat- equilateral tri- polygon?
00:07:58Equiangular polygon?
00:08:00Do you still remember it?
00:08:02S?:00]
00:08:03Yes. What does it mean? For- for- for the first type. I'll give you some hints. All the sides...?
00:08:10Are equal.
00:08:11All the sides are equal. Okay? All the sides of the polygons are equal.
00:08:16How about equiangular polygon?
00:08:17(inaudible)
00:08:18All the sizes of the angle?
00:08:21Are equal.
00:08:22Equal. Get it?
00:08:23Okay, I want you to try to help me to try to draw two types of polygon. They are four-sided and five-sided polygons.
00:08:41That is, equilateral but it is not equiangular.
00:08:45And it is equiangular and it is not equilateral.
00:08:50Okay, you try- take out, uh- clas- your classwork exercise book... to try to draw.
00:08:56And then I will ask you to come out and help me to draw the four-sided polygon. It is equilateral but it is not equiangular.
00:09:09Another four-sided polygon, it is equiangular but it is not equilateral. Okay?
00:09:17You try- you try to draw... in your classwork exercise book first.
00:09:45Okay, please be quick. Please be quick.
00:10:14Okay, can you get the meaning of the uh, questions? Can- can you get it?
00:10:18Yes, good. You- you try to draw... the uh, four-sided polygon, it is equilateral and it is not equiangular.
00:10:29Another four-sided polygon, it is equiangular and it is not equilateral. And also, for the five-sided polygon.
00:10:43That means, you have to draw four- four different diagrams. Four different diagrams.
00:11:42[ Bell ]
00:11:50Okay, I give you one more minute. And then would somebody come out to try to draw your answers on the board.
00:12:09Four- four different types of the diagram. The four-sided and also the five-sided.
00:13:11Okay? Have you finished?
00:13:14Okay, try to look at the board. I want you to draw a four-sided polygon, it is equilateral but it is not equiangular.
00:13:24Understand? It is not. And also, another four-sided polygon, it is equiangular but it is not equilateral. Got the point?
00:13:34Okay. Would someone come out and- and to draw.
00:13:44Okay, for this type. You try- try to come out and draw. Number six. Number six, yes.
00:13:54And then, uh, anoth- another one, this part. Twenty. Where's 20? Yes. Be careful of the wire.
00:14:06Okay, 32. Thirty-two.
00:14:09Hey, I want you to- to draw this one.
00:14:12Thirty-two.
00:14:16And then for equiangular, 19? Where's 19? Yeah, you.
00:14:49O- okay, we look at the four-sided polygon. Okay? We called it quadrilateral. Uh, I can use some mark to present it is equilateral.
00:15:02These four sides are equal. Okay, get it? Do you find that this angle is greater than 180 degrees?
00:15:12No, not- not- not 180. It's greater than 90 degrees. It is less than 90 degrees, so it's good.
00:15:21Okay, how about this one? Uh, this boy... used the mark to show that they are right angles.
00:15:32Can you find that the, uh- length between these two sides are different?
00:15:37Can you get the point? Okay, look- look- look at the five-sided polygon, we call it pentagon.
00:15:42What- what are the differences between them? Can you find out the difference?
00:15:47Uh, I am not satisfied with these two answers. I- I want another two to try to- to uh, to show that they are different. Okay?
00:15:59To show some differences between them. I want this pentagon equilateral but it is not equiangular.
00:16:08I want you to draw this five-sided polygon, it is equiangular but it is not equilateral. Okay, you try it again.
00:16:17Another two. Number 10. Try, yeah yeah. Come on.
00:16:28Number seven. Yeah, okay, you- you... okay, you draw it at the side. Yes. You draw it here.
00:16:48Ha ha ha. Yeah, thank you.
00:16:54Uh! Can you find the difference between them?
00:16:59Huh? Uh, a little bit. Okay, I- I- I- I try to draw another one for you. Okay, equiangular.
00:17:07Also the same, but this two sides... I draw it very short. Can you get it?
00:17:14And then I tell you- all the size- all the size of these five angles are equal. Can you get it?
00:17:23Okay, how about this one? I- I- I- I- I try- I try to draw it.
00:17:43Okay, this angle- two angles are 90 degrees. Okay? Can you get it?
00:17:48Do you find that uh- uh, the shape of this two five-sided polygons are different? Can you get it?
00:17:55Okay, I as- I ask you another question.
00:17:59If... can you- can you draw- can you draw a four-sided polygon, it is equilateral and it is equiangular? Okay? It is equilateral and it is equiangular.
00:18:24Can you?
00:18:39Okay, I want you to draw in this column. Can you help- help- help me to draw a four-sided polygon. It is equilateral and it is equiangular?
00:18:49A five-sided polygon, it is equiangular and also it is equilateral. Okay.
00:18:58Another two boys and girls to come out. Forty-two. No 42. Sorry. Your class have no- 25.
00:19:07Twenty-five. The first one. Yeah.
00:19:13Uh, 35, 25 and 35.
00:19:17Okay, 25, you draw on this box.
00:19:45Okay, thank you. Uh, the two boy show it to me that, uh, when you draw this four-sided polygon, the size of these four angles are- are equal.
00:19:57And the length of these four sides are equal. Okay, for this five-sided polygon, we called it a pentagon.
00:20:04This five sides are equal, this five angles are equal. Can you get it?
00:20:08Okay. How do we call such type of polygon?
00:20:14When it is equilateral and it is equiangular? You have learned this word before. In Form One.
00:20:21In- do you still remember? How- how- how do we call this kind of polygon?
00:20:26Square.
00:20:28Yes, anybody? Still remember? How many of you remember? Put up your hand. Let me know. Still remem- onl- only one?
00:20:37You have learned in Form One, okay. How- yes, how- how do we call such type of polygon?
00:20:44S?:00]
00:20:46Regular polygon. Okay, do you still remember the spelling?
00:20:50R-
00:20:51Try- try- try- try.
00:20:53Oh, your- your monitor try.
00:21:03Okay, thank you. Do you still remember this word?
00:21:07Okay, we read it together. Regular polygon. Regular polygon.
00:21:10Regular polygon.
00:21:12Once again, regular polygon.
00:21:13Regular polygon.
00:21:15Okay, what is meant by a regular polygon? That means the polygon is both equilateral and equiangular.
00:21:24We call- we call it a regular polygon. Okay?
00:21:29Do you still remember it? Yeah, okay. Uh, who's on duty today? Come out and help me to clean the board.
00:21:35We come to an- an- another- we try to discuss another properties of the uh- polygon.
00:21:45Uh, now, we come to discuss the sum of interior angles. The sum of interior angles of a polygon.
00:21:57Okay? Sum of interior angles of a polygon.
00:22:20Okay, sum of interior angles of polygon.
00:22:30Last week, last week. We have discussed the sum of interior angles... of a triangle. For the triangle, it is a three-sided polygon.
00:22:48Do you still remember the sum of the interior angles of a triangle? It is equal to...?
00:22:56One hundred and eighty degrees.
00:22:57One hundred and eighty degrees.
00:22:59Do you still remember the abbreviation? The- the abbreviation to describe such properties?
00:23:05Angle sum of triangle.
00:23:06Angle sum of triangle.
00:23:10Okay, angle sum of triangle. Okay.
00:23:13How about, uh- uh- for example, we have...
00:23:20We have a four-sided polygon.
00:23:27Okay? We have a four-sided polygon. We called quadrilateral, okay, for quadrilateral... what is the sum?
00:23:38What is the sum of interior angles of it?
00:23:42Okay, take out your classwork exercise book. Help me to find out the sum of interior angles of a four-sided polygon.
00:23:51I'll give you some hints. And you help me to work out the sum. First of all, I draw a dia- a diagonal A C inside the four-sided polygon.
00:24:06Okay? I call this angle, A two. This angle, A one. This B. It is uh, C two. It is C one. And it is angle D.
00:24:19Okay, help me to find out... I give you such hints.
00:24:24Help me to find out- to work out, the sum of angle A, angle B, angle C and angle D. It is the interior angle.
00:25:58Okay. Have you found out the sum of angle A, angle B, angle C and angle D?
00:26:06It means, what is the sum of interior angles of a four-sided polygon?
00:26:12I give you some hints. Help me to work out the sum of this polygon.
00:26:18For last week, you have learned the sum of interior angles of a triangle.
00:26:37Okay? Can somebody help me... to fill in the blanks? Anybody like?
00:26:50Number 13, you try- you try to fill in for- for the first line. Number 13? Where's number 13? Yeah.
00:26:57Okay, and then number 21. The second line. Okay, and then we come to the conclusion. How to present the conclusion?
00:27:16Okay, first of all, you say, A two plus B plus C two is equal to 180 degrees.
00:27:22You're using the properties- angles sum of triangle. Okay, also the second one.
00:27:27How about we come to the conclusion? How to work out angle A plus angle B plus angle C plus angle D?
00:27:35Okay, don't just only write down the answers. Show it to us, how to find out the answer. Seventeen.
00:27:43Have you- have you worked out the answer?
00:27:46Yes, okay, try- try- try to show it to us.
00:28:04Okay, thank you. Thank you. Yes.
00:28:08Okay, can you work out the sum- it is equal to 360 degrees?
00:28:13Yes, okay, how- how you got such answers?
00:28:17Why do you write down 180 degrees plus 180 degrees?
00:28:23Okay, angle A plus angle B plus angle C plus angle D.
00:28:26Do you find that it is equal to uh, A one plus A two plus angle B- plus B, angle C is equal to C one plus C two, can you get it?
00:28:34[ Bell ]
00:28:35And then plus D.
00:28:37Can you get it? And do you find that A one plus C one plus D is equal to 180 degrees?
00:28:44A two plus B and then plus C two is equal to 180 degree. Okay, we stop here.
00:28:51For a four-sided polygon, we find that, we can cut the four-sided polygon into two triangles.
00:29:00Cut it into two triangles, so we got- that the sum of interior angles is equal to the sum of the angles of two triangles. Can you get it?
00:29:11Okay, take out your textbook. We'll try to find out how to find the sum of interior angles of a pentagon, a five-sided polygon.
00:29:21Turn to page 31. Page 31. Okay, you try to work out the class practice number one.
00:29:30You can discuss with your classmate. How to find the pentagon?
00:29:34Okay, number one, it says, the dif- given figure shows a pentagon A B C D E.
00:29:39And then turn to page 32. It asks you to do something.
00:29:46Okay? Try to follow the question and work out the sum of interior angles of a pentagon.
00:29:59Uh, help me to- to- to clean the board. Please.
00:30:06Number one.
00:30:14Uh... is it done by you?
00:30:18No.
00:30:19No, okay, you- you clean it. You- you- you- you have to uh, uh- do it by yourself.
00:30:23Okay.
00:30:29Uh, is it done by you? It is not done by you?
00:30:35Yes.
00:30:36Yeah, yes.
00:30:42[ Bell ]
00:31:01Okay, we- uh, I- I say you- you- you try to finish this- number one first. We don't do number two.
00:31:08You try to finish number one to find out the sum of interior angles of a pentagon.
00:31:19Okay.
00:31:23Okay, uh, because it is time- time's up. So we have a quick look at number one.
00:31:34Okay, uh, first of all. First of all, we have a... pentagon. It is A B C D E, is it?
00:31:49Okay, and then turn to page 32. What does it say for question A?
00:31:54If two diagonals are drawn from vertex A to the nonadjacent vertices C and D, how many triangles are formed?
00:32:04It asks you to draw from vertex A to vertices C and D, how many triangles are formed?
00:32:13Three.
00:32:14Three. Okay, number B. What is the sum of the angles in each triangle?
00:32:19One hundred-
00:32:20One hundred and... 80 degrees.
00:32:21Eighty degrees.
00:32:22Okay, for the first triangle, the sum of the uh, uh, triangle is equal to 180 degrees-
00:32:27One hundred and eighty degrees, 180 degrees.
00:32:30Okay, number C. What is the total sum of the angles in all the triangles formed?
00:32:36What is the total sum of the angles of these three triangles? These three triangles.
00:32:41Five-
00:32:42One hundred and eighty degrees. One hundred and eighty degrees. One hundred and eighty degrees.
00:32:47Altogether, it is? Five hundred and forty degrees.
00:32:48Five hundred and forty degrees.
00:32:51Okay, we come to D. It is the conclusion. What is, therefore, the sum of the interior angles of this pentagon? It becomes?
00:32:59Five- 540 degrees.
00:33:00Five hundred and forty degrees. Okay, I stop here.
00:33:03You go home, try to- try to work out- find out the relationship, okay, between the sides-
00:33:12The number of sides of a pentagon and the sum of interior angle of that pentagon, okay?
00:33:18Mark down the homework for maths. You go home... try to finish page 30... two. Number two on your textbook.
00:33:30Okay? You work out in your textbook.
00:33:36Got it?
00:33:51Okay, class dismiss.
00:33:53Stand up.
00:34:00Goodbye class.