# AU2 CONGRUENCE

This eighth grade mathematics lesson focuses on developing student understanding of congruent triangles. It is the second lesson in a twelve-lesson unit of work focused on congruent triangles. The lesson is 47 minutes in duration. The lesson was taped in a girls' school. There are 26 students in the class.

TimeCaption
00:00:00Okay, um, we're doing revision from yesterday on the congruent triangle so do you remember what a con- what a pair of tria- congruent triangles are?
00:00:09Yep.
00:00:10Yeah.
00:00:11Two triangles that are the same.
00:00:12Same what?
00:00:15Same angles same sides.
00:00:16Same angles and same sides so we're doing 10 quick questions on this. So- all right, there's two right angle triangles.
00:00:27All right, and they're supposed to be the same. Supposed to look the same.
00:00:34All right, this one is A B C, and this one is D E and F. All right, they are congruent. So I'm going to ask you- ask you 10 quick questions on that.
00:00:49All right, number one, which angle is equal to angle A?
00:01:04Which angle is equal to angle D?
00:01:15Number three, if angle A is 30... and angle D is 60... uh, what size is angle E?
00:01:35And number four, what size is angle D?
00:01:49Which line is equal to B C?
00:01:56I'm sorry?
00:01:57Which line is equal to B C?
00:02:03Number six, which line is equal to E F?
00:02:14And... okay, if A C, if A B is five, all right, and B C is three, and A C is four centimeters, all right, how long is D F?
00:02:43Number eight, how long is E F?
00:02:51Number nine, the triangles A B C and F E D are congruent. Write that using the symbol. Do you want me to repeat it?
00:03:05Yeah.
00:03:05Triangle A B C and triangle F E D. And number 10, which is the hypotenuse of triangle A B C? The hypotenuse.
00:03:25Okay, who wants to answer them? Okay.
00:03:28Number one angle F.
00:03:30Yep.
00:03:31Number two angle C.
00:03:33Yes.
00:03:33Number three 60 degrees.
00:03:34Yes.
00:03:35Number four 90 degrees.
00:03:36Yes.
00:03:37Number five A D.
00:03:38Yep.
00:03:39Number six A B.
00:03:40Yes.
00:03:40Number seven four centimeters.
00:03:40Yes.
00:03:42Number eight five centimeters.
00:03:43Yes.
00:03:45Number nine triangle A B C is congruent to three lines.
00:03:50Three lines
00:03:50to triangle D E F.
00:03:53She hasn't got it right.
00:03:54Oh F E D.
00:03:57Triangle to- triangle what?
00:03:59F E D.
00:04:00D E F.
00:04:02You said F E D.
00:04:03Why did I say F E D?
00:04:07Because that tells (inaudible) the same.
00:04:10What's the same?
00:04:12Like F equals A.
00:04:14(inaudible)
00:04:15So F equals A and what's equal to C?
00:04:19D.
00:04:20D, and B equals E. So you've really got to write these in the same order.
00:04:24Oh.
00:04:25All right?
00:04:25And 10 is A B.
00:04:26Why?
00:04:28Ten is A B. Just to show the congruence to show the relationship between them.
00:04:31I'm doing them in alphabetical order.
00:04:33I know. And I didn't say it that way did I? Who got them all right? That's pretty good. Who got nine right?
00:04:40Yeah I did.
00:04:42Yeah, right. Number 10 was A B.
00:04:45Nine.
00:04:46All right, okay, I've got a worksheet for you to do and you've got to work in groups of three or four. So that'll be that group.
00:04:59So if you two Angela and Laura, if you can come down the front and work with the front two. Just bring your chairs down, don't worry about-
00:05:14What do you need? You need your protractors. You can bring a desk down if you want a little bit more room to work on or you might just move your pencils.
00:05:38Just turn around till I finish talking to you, all right? So you've got five here.
00:05:45Yeah, one, two.
00:05:47Oh that'll do. That'll be all right. Can you talk together?
00:05:52Where did you want us to move?
00:05:53Um, yes. Yeah, one of you move down there one so you've got a group of three and one of you can move- work with one of these.
00:06:01All right Angela, you can work with um Eun and- all right?
00:06:10Then you've got just one down there. Here's a- All right?
00:06:17How am I going to work?
00:06:19Bring a chair. Yeah, you can bring that- yeah, bring the table over.
00:06:25(inaudible)
00:06:27No.
00:06:36All right, I'll go through the instructions with you.
00:06:52I'll read through the instructions and girls, read through the instructions as I go through it.
00:06:57What you're doing is you're actually finding the rules for a pair of congruent triangles and you're trying to find the minimum rules.
00:07:05So the task you need to produce a list of instructions so that anyone following them will construct exactly the same triangle.
00:07:12Oh.
00:07:12It's got a list of what you need. And the first part, steps one and two, each person in the group on the piece of paper on the back here it says your triangle.
00:07:22You construct a triangle on that page without showing the rest of your group and you write down the steps of how you did it. All right?
00:07:32Then, after everybody's done that in your group, um, you take turns to read your instructions out to the group and they can use the pink, um, the paper at the back.
00:07:44I've done a variety of colors. You should be able to fit three on one page but I've given you an extra page as well in case you can't.
00:07:51So you will be drawing three triangles or two. If there's two in the group you'll be- if there's three in the group you'll be drawing the other two triangles.
00:07:58If there's four in the group you'll be drawing three.
00:08:01So one person say Laura here will read out her instructions and the other two will actually follow her instructions, all right?
00:08:10If you then when she's finished you have a look at it and see if they're exactly the same. If they're not you can go back and change your instructions so that they actually work.
00:08:20All right? And then each other person in the group does that. So each person takes a turn to read out their instructions to the others in the group and they follow it.
00:08:29You're not to actually look at what they did. You actually have to follow the instructions.
00:08:34Do you make up instructions (inaudible)?
00:08:37No, you make up your own instructions, it depends on what you're drawing. All right, you make up your own triangle.
00:08:42And what you're going to end up with is a minimum set of instructions so that the least number of steps that you need to draw your triangle.
00:08:51Now there's four different ways of doing it. So if there's three or four of you, you might end up with totally different ways.
00:08:59So you've got to decide what- how- what you need for the minimum number of steps for your triangle, all right?
00:09:06Is it going to be all sides, is it going to be all angles, what is it going to be? Is it going to be all six? Do you need all six angles and all six sides?
00:09:17All right so go ahead, let's start that. So you've got to draw your triangle first on the second page and then write down your instructions.
00:09:27(inaudible) Is there one in the drawer?
00:09:30Don't think so, just borrow. No. Just borrow one.
00:09:48Draw your triangle first. All right? Draw your triangle first. You draw it on the second sheet, the top of the second sheet.
00:10:00Yep.
00:10:00Do- you need to draw two don't you?
00:10:03No, just one.
00:10:05So miss the person that's giving the instructions (inaudible).
00:10:09You draw the triangle first yes. Everyone draws a triangle and writes down their instructions.
00:10:13All right.
00:10:27So you want us to draw one triangle?
00:10:29Just one triangle.
00:10:37Do you draw the triangle like this?
00:10:40You ha- yeah, you use your protractor and your compass to draw the triangle.
00:10:43Can I trace this?
00:10:45You can. Yeah.
00:10:47Okay I'll use it after.
00:10:49But you're not going to draw the same triangle are you?
00:10:50No.
00:10:51No. All right, and how are you going to know what size the angle is? By the length of the line.
00:11:41Yeah.
00:11:42Can I sharpen the pencil?
00:11:43Yeah, that's all right, yep. Just go and sharpen it.
00:11:47(inaudible)
00:11:47Pardon?
00:11:48I said I don't want to get up in front of the camera.
00:11:49Yes you can.
00:12:35I'm just waiting for a compass.
00:12:37Is that what we're going to be doing finding the angles and stuff.
00:12:39It's not going to be the same one as Kate's is it? Yeah, you've got to find- it depends on how you're going to draw it. How you want them to draw it?
00:12:48You can either find angles or you can find sides.
00:12:50Okay.
00:12:51Or a combination of both.
00:12:53So I could write all my angles and all my sides couldn't I?
00:12:56You could but that's not the minimum number.
00:12:58Oh so you-
00:12:58So you've got to end up with the minimum number that you need. So what stage have they drawn your triangle without you having to add on the rest of the instructions?
00:13:06You might have a lot of instructions to start with and then you find after a couple that they've actually drawn it.
00:13:11Okay.
00:13:12All right? Yeah.
00:14:14You should be doing yours up here.
00:14:16I am.
00:14:16All righty, okay. Now you shouldn't be looking. You're not supposed to know what it looks like.
00:14:26Um, I need to make a measurement. When I measured it, it's like that (inaudible) Do I write like five point whatever?
00:14:32Yes, you'll have to, yeah.
00:14:33Okay.
00:14:39(inaudible) I'm up to you.
00:14:50Have you finished? Have you all finished?
00:14:53Yeah.
00:14:58When you all or uh three or four of you have finished the triangle, you can start- the first person can start reading theirs out.
00:15:05Okay, can I read mine out now?
00:15:06If the rest are finished, yes. Has Jessica finished?
00:15:10(inaudible)
00:15:14Yes, Miss. Um- when we write the instructions will it be in here? And um, when we write it would it be- draw up a five point six centimeter-
00:15:24It's- it's whatever your instructions are going to be. It can be a combination of side- size of the length of sides or angles.
00:15:33Miss?
00:15:34Depends on what you want to do.
00:15:36How many instructions do we have to have?
00:15:38You're going to try them and find out. They're going to try them. If they don't draw the same as what you've got, it wasn't. If it- if they draw the same it was right. Okay?
00:15:48Yep.
00:16:05Is that right just like- draw
00:16:07Yeah, right here. Yeah, yeah.
00:16:08A line.
00:16:08Yeah, well you've got to read it out to the other two now, they're not to know what you have got.
00:16:12I know but-
00:16:13Yes.
00:16:13Is that- is that all you have to do?
00:16:14Yes.
00:16:15Oh okay.
00:16:17Righty-o.
00:16:21Is mine right?
00:16:23It depends, if it works, if they draw the same triangle as you've got it works. If not you change it. All right? So you've got to try it.
00:16:34Okay (inaudible).
00:16:45It doesn't work.
00:16:46She's deliberately not responding.
00:16:48I'm responding! She's like (inaudible) because (inaudible).
00:16:50Draw a half circle.
00:16:51I said- uh.
00:16:53Okay.
00:16:53Yes, there you go.
00:16:54Okay, now go to H.
00:16:58Yes.
00:17:07Yes.
00:17:08Okay, have you done that?
00:17:10Yes.
00:17:11Now, draw an arc from H bisecting the arc from S.
00:17:19Okay.
00:17:20Using your compass, measure the distance from (inaudible).
00:17:22Okay, now- you ready for this? That was (inaudible) point N, so write point N. Now draw- Now draw a line from N to S.
00:17:36Yes.
00:17:37Okay, all right, trace a set square... but it's two minimum isn't it?
00:17:41No, no, I don't want that.
00:17:43That's why I didn't think you wanted.
00:17:44I want lines and angles.
00:17:45That's what I thought.
00:17:46All right?
00:17:46Yep.
00:17:47Because they might have a different size set square.
00:17:49Okay. Oh, yeah.
00:17:51True?
00:17:51Yep.
00:17:52Yeah.
00:17:52Okay.
00:17:55So when you have all finished your instructions you can start reading them out.
00:18:19Now you've gotta cut them out and paste them on and see if they fit. All right? And then you get to keep them. You can paste them down here. All right?
00:18:46Did it work?
00:18:46Well I knew how to say radius but I had to say it wasn't (inaudible).
00:18:49All right, because if it- if they've worked, you need to cut them out and give them back to Jessica.
00:18:53We're going to do them after.
00:18:54All righty-o, okay.
00:18:55So we're doing one.
00:18:59This- just- make a radius of five centimeters.
00:19:09I think mine's right.
00:19:10You'll find out won't you?
00:19:12Yep.
00:19:12Can you- can you- can you bi- I drew a line.
00:19:14Yes.
00:19:15And I sort of bisected...
00:19:19So did you decide that that was important or the length of the line was important?
00:19:25The length of the line- oh, no the angles.
00:19:27Angles so that's all you- so try that. All right?
00:19:36Interval A B is vertical and measures five centimeters.
00:19:41A B.
00:19:42Yeah, interval A B is vertical and measures five centimeters.
00:19:53I think you can see they're pretty right, can't you?
00:19:55Interval A C is horizontal, and it measures three centimeters.
00:20:33So did it work?
00:20:35Uhh, no because (inaudible).
00:20:40Interesting but are they congruent? Cut them out and have a look. If they fit on top.
00:20:44They're the same but...
00:20:47It's the same but-
00:20:47Yeah, that's right so- so cut them out. She didn't have to did she?
00:20:53She's got nice paper.
00:20:54Oh sorry. You could've swapped. Do you want a different color?
00:20:58I'm kidding no. So that's right. They're- they're congruent.
00:21:03So you cut them out and give them- is it yours Natalie?
00:21:06That's mine that's mine.
00:21:07All right so you um- you can cut them out and give them to Louise and she can paste them on hers. All right, yeah.
00:21:16Is um- is this congruent? Because I wasn't here on Tuesday.
00:21:18Pardon?
00:21:20Yeah what's a con- congruent triangles are triangles that have the sa- exactly the same sides, three sides are equal and three angles are equal.
00:21:27I don't cut this out do I?
00:21:29No, you- you cut the other two out and put them. But you can cut these out. All right? She can cut- Natalie can cut hers out.
00:21:37Oh, can I cut this out?
00:21:37Oh all right.
00:21:40This is mine.
00:21:43That's mine.
00:21:54So have you done one yet?
00:21:55Yeah we've done two.
00:21:56All right.
00:21:58(inaudible)
00:21:58Okay.
00:21:59Hang on.
00:22:09I've figured it out Miss.
00:22:12[laughs]
00:22:12I think anyways. I- I'm doing the- the measurements.
00:22:16Righty-o. You don't have to do the measurements. You can make combinations.
00:22:23Oh, I don't get this.
00:22:26Let's get the triangle and measure everything.
00:22:28Yeah and- and do the instructions on how to make it.
00:22:31Okay well what's the (inaudible) gonna be because (inaudible).
00:22:35That's fine. Yeah, all right?
00:22:59So have you done two?
00:23:01One (inaudible).
00:23:08Eight point seven centimeters.
00:23:11I don't think that was necessary.
00:23:13Mine's like five centimeters long.
00:23:15Mine's eight point seven.
00:23:16Jessica.
00:23:17Mine's eight point five.
00:23:20Do you- are you using- yeah, a compass to draw the-
00:23:24We would have to measure the (inaudible).
00:23:25Ah, right.
00:23:26(inaudible)
00:23:27It was 60 degrees
00:23:28That's all right.
00:23:29And it was six centimeters long.
00:23:31And then-
00:23:32Six.
00:23:33Draw a line from the top down to the (inaudible).
00:23:36Draw a line at 40 degrees that is five point one centimeters long.
00:24:03Miss what should we do now?
00:24:04Pardon?
00:24:04What should we do now?
00:24:05Have you done all of them have you?
00:24:05Yep.
00:24:06Yeah.
00:24:07Well, did you end up working out how many instructions you actually needed for each one?
00:24:12Yep, I needed four.
00:24:15You needed four, what were they?
00:24:16Um, interval A B is vertical and measures five centimeters. Interval A C is horizontal (inaudible).
00:24:25So if it's saying horizontal it's saying it's at an angle aren't you?
00:24:31Yeah.
00:24:31So we're saying one's vertical and one's horizontal.
00:24:33Yeah and you um...
00:24:34Then you're defining the angle between them aren't you?
00:24:36Mm, I'm saying it's a right angle.
00:24:38Yes.
00:24:39Because interval- interval A B C is a right angle.
00:24:44Right, so did they need all those instructions to finish your triangle?
00:24:47Yes.
00:24:48Yes.
00:24:49Draw an arc from angle, uh, angle C joining to the B C which is the hypotenuse and draw a dot in any (inaudible).
00:24:56All right, so you started with a line that was vertical.
00:24:58Yep.
00:24:58And then a line that was horizontal of a certain length.
00:25:00Yep.
00:25:00And then you joined them.
00:25:03Yes.
00:25:04So what did you-
00:25:05And it was a right angle.
00:25:07Yes, and the right angle so you had two sides and a right angle and then joined them.
00:25:10Yeah, and then-
00:25:11The arc on- the arc on angle C and then join the interval-
00:25:11And then joined them.
00:25:15Did you- what was the arc on angle C? Show me. Right, did you actually have to have- so did you tell them what length that was?
00:25:24No. I just said join it.
00:25:25No, you didn't have to.
00:25:26Which is the hypotenuse.
00:25:26Join it, yes. Yes, so you only needed two sides and the right angle.
00:25:30Yep.
00:25:31Okay. What did you need?
00:25:33Three.
00:25:34And what was it?
00:25:35Okay, I took my set square and drew a straight line nine centimeters for the base. Um, number two, I then made 90 degrees set square-
00:25:42Pardon? It's, well how long was the base, did you say?
00:25:46Um, nine centimeters.
00:25:47Right. Yes. And so you drew a right angle as well?
00:25:50Yeah.
00:25:51Yes.
00:25:52Um, number two, I then made 90 degrees set square- along the line, the end on the corner, and drew a straight line up six point two centimeters.
00:26:01Yes.
00:26:02Number three I then joined the- both ends up with the right angle triangle-
00:26:07So you had the same thing, you had a right angle and two sides.
00:26:10Yeah. And the degrees were 90 degrees so-
00:26:11Right.
00:26:12Did you have anything different?
00:26:14Nope.
00:26:15Almost.
00:26:16You all did right angles.
00:26:17Yep.
00:26:22So no imagination.
00:26:23Nope.
00:26:26[laughs] All right. So that's one of the- think and see if you can think of the same triangle if you could've given different instructions to have done the same triangle.
00:26:38Yep.
00:26:43See if you can all end up with different ideas.
00:26:46Okay.
00:26:53So how did you end up?
00:26:54Good.
00:26:54Good. We all won.
00:26:55We have to check them.
00:26:56I won.
00:26:57No we all won.
00:26:59Yeah, were- were they all different?
00:27:00No, they're all the same.
00:27:01They're all the same. So what was the same? What did you end up having to write?
00:27:05Construct a right angle-
00:27:07What did you end up having to draw?
00:27:09Oh.
00:27:09Triangles.
00:27:10Yeah.
00:27:11Congruent triangles, they're all congruent.
00:27:13Yes, but what were the instructions?
00:27:15Um, I couldn't- um... Draw an eight-centimeter line.
00:27:19Yes.
00:27:21Um, make a radius of five centimeters.
00:27:23Mm hm. Yeah.
00:27:26She did not say that.
00:27:27Yeah, that's all right.
00:27:27Um, place the point of the compass at the right end of the line and draw a circle.
00:27:32Yes. Of what size?
00:27:34Pardon?
00:27:35Yeah.
00:27:35Um, with a five centimeter radius.
00:27:36Yeah.
00:27:37Um, uh- and make a... where am I? Oh, make a seven-centimeter radius and draw a circle from the left end of the line.
00:27:46Yes
00:27:46And join where the point-
00:27:48So what did you end up doing?
00:27:50The edited version.
00:27:52Was it all the sides, all the angles, a combination?
00:27:55Pardon?
00:27:56What did you end up with?
00:27:57All the same sides and angles.
00:27:59All the sides, yeah. Yep you end up with all the same angles but what did you tell them to draw, sides or angles?
00:28:03Um, sides.
00:28:04All sides.
00:28:05Yeah.
00:28:05Did you draw all sides?
00:28:06Um, I said an angle of 60 degrees and then but- and then two lines.
00:28:13Which lines?
00:28:14The beginning line.
00:28:15Yes.
00:28:15Was A B 10 centimeters long.
00:28:16Yes.
00:28:17And then an angle of 60 degrees at A.
00:28:19Yes.
00:28:20And draw a line six centimeters long.
00:28:21From where?
00:28:22From A.
00:28:22From A, yep. So you've got two lines and an angle.
00:28:26Yes.
00:28:26Righty-o. And what did you end up with Tanya?
00:28:28Uh...
00:28:29Yours were all lines as well?
00:28:30Yes. Draw an eight-centimeter interval.
00:28:33Right.
00:28:33Make a radius of five centimeters, draw an arc, make a radius of six. Draw an arc from H bisecting arc from X to form point N.
00:28:41Bisect- oh, you mean intersecting.
00:28:43Oh, crumbs.
00:28:44Yeah. [laughs] So you'd end up with three sides.
00:28:48No, no yes, it was-
00:28:49Yeah, righty-o.
00:28:50What's the difference between bisect and...?
00:28:53Bisecting means to cut it in half.
00:28:54Half, yeah. Bi- bi.
00:28:55But it did bisect it.
00:28:57It cut it in half.
00:28:58It depends on how long the line is.
00:29:00It was half a line.
00:29:02[laughs] Yes Louise.
00:29:04How many times do you have to go through them?
00:29:06Just once. You have to do one each. Are you finished?
00:29:08Is that all?
00:29:09Yes.
00:29:09She's just go to do hers.
00:29:11Righty-o.
00:29:13We did all ours and they all figured it out.
00:29:15Yes.
00:29:15Um... with Louise's, we did-
00:29:21When you cut them out you usually cut them out to see if they fit?
00:29:25Yeah, but
00:29:25but they- the angles were all the same. We measured the angles and all that.
00:29:25Yeah
00:29:26Yeah, that's all right. Yes. Righty-o.
00:29:28Um, with Louise's, she didn't give us any angles.
00:29:32Yeah, that's okay.
00:29:33But with um mine I gave the angles, is that- is that all right?
00:29:37So which angles do you- which angles did you give?
00:29:40I gave a five centimeter line and then a right angle with another five centimeter line.
00:29:42Yes.
00:29:44Right, okay. And did you do anything different Nerida?
00:29:47Yes, and Nerida's is good.
00:29:48I like Nerida's. Oh, sorry.
00:29:50Um-
00:29:51I started with a six centimeter line going horizontally.
00:29:54Yes.
00:29:55And then found halfway three centimeters and put a dot.
00:30:00You put the center point of a protractor on the dot.
00:30:03Yes.
00:30:03And then you uh find 70 degrees.
00:30:06Yes.
00:30:07And you draw a line then put a dot. Then you connect um the top point to the bottom right point of the six-centimeter line.
00:30:15Right. Yeah.
00:30:16And Nerida's- see how she has (inaudible) like that.
00:30:18Yes. Yes.
00:30:19And then you- you put the pencil on the top dot again, and draw it to the (inaudible) left hand side.
00:30:26Well that was very different.
00:30:27I liked hers cause she had like-
00:30:28Yeah. Yeah. So you really- what was the minimum number of instructions? So you ended up with an angle there didn't you?
00:30:36Yep.
00:30:37And that was a length so it determined a- a point didn't it? So really you've drawn that triangle first haven't you? Haven't you?
00:30:45Yeah.
00:30:45Yeah, so it's- it's that line and that line drawing that angle. So you've ended up with two triangles.
00:30:50Yep.
00:30:51That one and that one.
00:30:52Yep.
00:30:52That one had a line a line and an angle.
00:30:56Yep.
00:30:57That one had an angle a line and a line as well.
00:30:59Yep.
00:31:00All right?
00:31:08Is everyone nearly finished?
00:31:09Yes.
00:31:10So far we've only had two types. There's four. There's four types that you can do.
00:31:23If I've had a look at yours... girls, if I've had a look at yours, see if you can draw the same triangle in a different way using different instructions.
00:31:36Do we write down those as well?
00:31:37You can right next to it yes.
00:31:40How did you go with yours? What did you end up with? But what did you draw?
00:31:47I drew a triangle.
00:31:52A six centimeter line and then I just used compass points and joined them.
00:31:54So you just did three sides? The length of three sides.
00:31:58No, I- but I didn't include the length of- length.
00:32:02Yes.
00:32:02I just- I just said um draw a six centimeter line set your compass to three centimeters, and draw an arc from each end and draw it.
00:32:10So, that one's three centimeters and how long is that one?
00:32:13I don't know the compa- yeah, that'd be three centimeters.
00:32:16Both of them are three. So you've done two- the length of the bottom line and the length of each side.
00:32:21No, the length of this- like how much apart (inaudible).
00:32:24Yeah well that's- that determines the length of a line doesn't it?
00:32:26Yeah.
00:32:27Yeah.
00:32:27So what have you done, the same?
00:32:28No um...
00:32:30You've done something different?
00:32:31Used a ruler and protractor.
00:32:32And what did you do?
00:32:34Um, did eight centimeter line.
00:32:37Yes.
00:32:37And then I got the protractor and did 60 degrees.
00:32:40Yes.
00:32:41And join that and then join these together and found the measurements of the-
00:32:44So you found the length of that?
00:32:45Yeah, six centimeters.
00:32:45Right, so it's two sides and an angle.
00:32:47Yeah.
00:32:48Yeah. All right.
00:32:55All right girls, we'll stop now. And I'll discuss what you've been doing.
00:33:05All right, there's been basically two different sorts that have come out.
00:33:11All right, first of all most people are starting with a line of a certain length and lots of you are drawing, um another line here of a certain height-
00:33:21I'll- probably make this cross first.
00:33:22You're saying how long that will be by drawing an arc from the point, and you're saying how long the second line will be by drawing another arc from the end of the other point.
00:33:32And you're joining it up. So you're defining the length of the three sides. Okay?
00:33:39So three sides. And there's another one that a lot of people have been doing which is the one that Justine did. What's yours Justine?
00:33:50Um, with a protractor.
00:33:52Yeah.
00:33:52Yeah.
00:33:53First of all you started with a line didn't you?
00:33:54Oh yeah.
00:33:55Yep.
00:33:56And then 60 degrees.
00:33:58Right, so you draw a line 60 degrees here.
00:34:03And then that's six centimeters.
00:34:05So then you determine the length of the line and then you join those up.
00:34:08So what she's done is what a lot of other people have done. If you got the line, that line, so two sides and an angle.
00:34:20In every single one of those that worked where did you notice the angle was?
00:34:24(inaudible)
00:34:25In between the two lines, in the middle, all right? So the angle had to be between the two lines.
00:34:30Yes I put that in my notes- two sides must be of the angle.
00:34:35That's good. Must- two sides must be.
00:34:37The two- like the two- cause you said the minimum and I said the two sides must be of the angle.
00:34:39Yeah.
00:34:42All right, so it's the two sides of the angle, yes.
00:34:44Yeah.
00:34:45Some people have done the angle on the left. Some people have made it a right angle but they're still defining it. There's two other ways of doing it. Helen.
00:34:53Is it different if you just- if you say both angles?
00:34:56Yes it is.
00:34:57I just did it that way because you said (inaudible).
00:35:00Yeah. So you've got a- a line.
00:35:01A line and then A B.
00:35:03A B.
00:35:05And at A you make it 60 degrees and just draw a line intersecting.
00:35:08Yes.
00:35:10And at B you'd make an angle 37 degrees.
00:35:13Yep.
00:35:13Until their intersecting.
00:35:15So that's another way of doing it. Yes Kate?
00:35:19Uh, another way is you get-
00:35:21Hang on- I'll just write this one up. A side and two angles, all right? And what's the other one Kate?
00:35:29And you draw a 90 degree angle
00:35:31Yes
00:35:31And you join the other side up.
00:35:33And you join the other side up.
00:35:34Join the two ends.
00:35:35Right, you've got a 90 degree angle, what are you going to define? What else are you going to tell me? You said I've got a 90 degree angle, what else are you going to tell me?
00:35:44The length.
00:35:45The length of the sides. So you've got the length of that side and the length of that side, is that the same as anything I've done?
00:35:52No.
00:35:56(inaudible)
00:35:57Like the bisecting ones.
00:35:59You've got the bisecting one.
00:36:01The two sides and an angle.
00:36:02It's like the two sides and angle, only the angle this time is 90. But it is to do with a right angle. The right angle can be special. Yes.
00:36:14Is it (inaudible)?
00:36:16No.
00:36:17Doesn't- doesn't the two angles add up-
00:36:19Yeah.
00:36:19Yes yes, that's right. The- the angle up the top.
00:36:23Yeah.
00:36:24Has- those two angles have to add up to 90 degrees.
00:36:26They have to add up to 90 degrees, but if I define the three angles will I get congruent triangles?
00:36:33Um...
00:36:34Yes.
00:36:35No.
00:36:36Why not?
00:36:37Because they'll be different lengths.
00:36:39They could be different lengths so I could have another one exactly the same only smaller with the same three angles. So three angles is no good.
00:36:52But I've still got this right angle here. I can define it as two sides and an angle, or I can also define one side and the other side,
00:37:04the hypotenuse and it will always be the same with a right angle triangle.
00:37:10All right? So this one is written as S A S, side angle side. And the A goes in the middle to show you that the angle has to be between the two sides. This one is written as, can you guess?
00:37:27S S S.
00:37:28S S S. This one?
00:37:32A A S.
00:37:34A A S or S A A, yep. And the last one is R for right angle, H for hypotenuse and S for side. All right, it doesn't matter which side.
00:37:48All right, I just want you to start activity... yeah uh by the way to finish this off, paste those triangles in here that match yours. All right?
00:38:02And... in your book... page 343... 343.
00:38:30No, you did the other.
00:38:31All right, page 343, this- number one, two, three and four explains what we've been doing
00:38:38so if you need to go and read those you can but I want you to start activity seventeen point one.
00:38:44And where it says for number one it says are these triangles congruent? Why? I just want you to write S S S, S A S, A A S or R H S, whichever applies.
00:38:59So the first one, what- which one will it be? Question one on activity seventeen point one.
00:39:06S S-
00:39:06Miss, can I (inaudible)?
00:39:07Yeah. Yep.
00:39:09What is S S S?
00:39:12(inaudible)
00:39:17Girls, just listen please. Number one, it says are these triangles congruent, why. Some people have been calling out. It's S S S because the three sides are equal. Can you see that?
00:39:29Oh.
00:39:29And which- and you've got to name the pairs of equal corresponding angles. So when it says are these triangles congruent and it says why just say S S S.
00:39:38So start activity seventeen point one if you've got any questions, I'll ask you.
00:39:54You said that was due Friday.
00:39:56No, I said it was due today. Your homework you had to do the investigation activity.
00:40:02(inaudible)
00:40:03Yeah. Just want to check if you've done it. So-
00:40:37Is anyone away today? I don't think so, no.
00:40:41Okay, so, did you do your homework?
00:40:46How's that? That- that.
00:40:49Yeah you just had to do some- you had to do this. Yeah. All right? It was pretty easy you just had to say which sides were equal.
00:41:05Right- right ha- right angle, hypotenuse and a side. All right? I'll write these down next lesson anyhow and go over it.
00:41:14Oh.
00:41:14Girls, I'll go over these rules next lesson and write them down. But I just want you to start some of the examples.
00:41:19Did you do your homework? Good. Elise?
00:41:25(inaudible)
00:41:36Yes.
00:41:37Good.
00:41:38I did- actually I accidentally did two and two as well. Like I did number two on the other page too.
00:41:44These ones?
00:41:45(inaudible)
00:41:46No I did these ones too.
00:41:48All right, that's all right. That's basically what we're doing today. Did you realize?
00:41:53Yes.
00:41:53So you should have been clued up. You should've known the other two. Right. Have you done your homework?
00:42:03Um, yes I did. I did those and these chapter seven through (inaudible).
00:42:08Yes. Yeah you did exactly the same thing Helen.
00:42:10Um, yeah.
00:42:11Okay.
00:42:13D equals D.
00:42:15(inaudible) Okay.
00:42:19Which activity is it?
00:42:21Seventeen point one you're doing.
00:42:23That's not 17, oh.
00:42:24Yeah. So- just start those.
00:42:27Okay.
00:42:28All right, did you do your homework? Good, okay.
00:42:31It's very messy.
00:42:32That's all right.
00:42:40Kate?
00:42:41Good. Mikala?
00:42:41Yeah.
00:42:46I did the other homework.
00:42:47The other homework? Oh, righty-o, good. Okay, that's when you didn't do it the other day.
00:42:52Yeah.
00:42:53I'll tick that off. All right. I always give you a tick above the cross if you do it again.
00:43:01Elise, you did- weren't here.
00:43:03I was in bed.
00:43:04Pardon?
00:43:05I was in bed with mumps.
00:43:06You've been sick haven't you? So you know- you understand what we're doing today?
00:43:13No.
00:43:14Even though you missed the lesson? Congruent triangles have exactly the same three sides equal and three angles equal.
00:43:20Oh.
00:43:20So go over the work that we did. Have a look at the beginning of the chapter of it, and it will say that- um- that sheet I gave you.
00:43:27Oh, okay.
00:43:28That's basically all it is. So it's just saying three sides are equal and three angles are equal.
00:43:31Oh okay, that's pretty easy.
00:43:33Yeah. How'd you go with the revision at beginning of the lesson?
00:43:39Um, (inaudible).
00:43:41Got a few right?
00:43:42(inaudible)
00:43:43Oh good, that's all right.
00:43:45Nicole, did you do your homework?
00:43:46Yeah.
00:43:47Good.
00:44:00Did you do your homework Mary? Okay. So you did it, okay.
00:44:10No I wasn't here and I didn't know about it.
00:44:12Yeah?
00:44:13I wasn't here.
00:44:15Righty-o. You were here last lesson.
00:44:17No.
00:44:18I- I was away.
00:44:19Um, all right, okay.
00:44:19She was away.
00:44:31That's the end of the lesson. All right, I'll just check- girls, can you- did everyone else do their homework?
00:44:37I haven't got around to checking you all. Who didn't? You were away that's all right Natalie. So everyone else did it? Marisa?
00:44:46For homework I just want you to um do down to the bottom of the page down to number four. Yep.
00:45:01What page were we on?
00:45:02Page 344. For homework... to the bottom of the page. All right, that's due Friday, tomorrow. I'll take your books tomorrow too. I didn't collect them last lesson.
00:45:28All right girls you may go.
00:45:32Miss, what do we do with these?
00:45:34You keep them and put them in your book. Don't lose them.
00:45:50Um, do we have maths tomorrow?
00:45:52I think so. Why?
00:45:55Well, because I'm not going to be here tomorrow. I'm going to Newcastle.
00:45:57Going to where?
00:45:58Newcastle.
00:45:59All right, what for, anything interesting?
00:46:01Uh, yeah, my sister's (inaudible) competition, and (inaudible).
00:46:07So just do a- finish that- that time exercise. Yeah.
00:46:12Okay well I'm trying to find my (inaudible).
00:46:14We'll know what you're up to.
00:46:15Okay.