US87 (from TIMSS 1995 Video Study)

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This lesson is on interior angles of a polygon.

The lesson was released following the TIMSS 1995 Video Study and is included here because of high interest in it among educators. Resource materials from the lesson are not available

TimeCaption
00:00:02What is the angle that is vertical to the seventy-degree angle?
00:00:07Vertical angles are formed by what, Juan?
00:00:10I don't know. I was just stretching.
00:00:13Don't get nervous. He's just stretching.
00:00:15When I intersect lines, I get vertical angles, right? Look at your definitions. I gave them to you. You have them there. You can look them up.
00:00:27Here we have vertical angles and supplementary angles.
00:00:30Angle A is vertical to which angle?
00:00:34Seventy.
00:00:35Therefore angle A must be...
00:00:38Seventy.
00:00:38Seventy degrees. Go from there. Now you have supplementary angles, don't you?
00:00:44What angle is supplementary to angle B?
00:00:48A.
00:00:49I mean, I'm sorry. Angle A.
00:00:50B.
00:00:51B is and so is?
00:00:52S//C.
00:00:52//C. Supplementary angles add up to what number?
00:00:58One eighty.
00:00:59One hundred eighty degrees. So if you know one is seventy,
00:01:02the other one has to be?
00:01:04Hundred ten.
00:01:04A hundred ten. Go from there.
00:01:06Okay, you have all your information,
00:01:09so we already figured these out.
00:01:11We have the measure of angle A is seventy degrees.
00:01:15B is a hundred ten and C is a hundred and ten. We know that.
00:01:21What information are we given in the second problem for D?
00:01:25Fifty-three degrees.
00:01:27Okay. Two things. You have fifty-three degrees.
00:01:31What is the other angle I've indicated in there?
00:01:34 Mike?
00:01:35Right angle.
00:01:36It's a right angle which add up to?
00:01:37Ninety.
00:01:37Ninety degrees. Okay?
00:01:40What's left?
00:01:43Somebody just gave me the answer.
00:01:45Thirty-seven.
00:01:45Thirty-seven degrees, right?
00:01:50Why thirty-seven degrees, Jamie?
00:01:54Carrie?
00:01:55Because thirty-seven and fifty-three equals ninety.
00:01:59Thirty-seven and fifty-three equals ninety. The middle angle is ninety
00:02:02and why did they all have to add up to one eighty?
00:02:05Because it's- it's a-
00:02:07Because it's a? Veronica.
00:02:10What is this angle called here?
00:02:12A straight.
00:02:13A straight angle. And a straight angle adds up to?
00:02:15One eighty.
00:02:15One eighty.
00:02:16Okay, you think, in a couple of minutes, you can figure out the rest of them?
00:02:20I think so.
00:02:33Is E, F, and G a bit confusing?
00:02:35How many right angles do you see in that-
00:02:37Two.
00:02:38There are two right angles, right?
00:02:40Yeah.
00:02:40Okay.
00:03:00Okay, you want some prompting on this one?
00:03:03Question? Carrie, what?
00:03:06I don't understand which one's you're supposed to-
00:03:08Which ones are the right angles?
00:03:08Yeah.
00:03:09Okay, I have a right angle here...
00:03:13This angle right here is a right angle...
00:03:16and this angle here- I should of used colored chalk.
00:03:19This angle here is a right angle. Okay.
00:03:22So work backwards.
00:03:23If this angle here is a right angle and this is thirty degrees,
00:03:26what does G have to be?
00:03:28Sixty?
00:03:28G has to be?
00:03:30Sixty.
00:03:30Sixty. Okay?
00:03:37If this angle is also a right angle in here and this is thirty,
00:03:41what does F have to be?
00:03:42Sixty.
00:03:43Sixty.
00:03:45And what's left then for angle E?
00:03:50Thirty.
00:03:51They all have to add up to?
00:03:54Okay, so if we have a sixty-degree angle and this-
00:03:58If this angle is a right angle ... what about this on the other side?
00:04:03That also has to be a right angle, doesn't it?
00:04:06Yeah.
00:04:07Because ninety plus ninety is?
00:04:09A hundred eight-
00:04:09One eighty. So what we have left for E is another thirty-degree angle.
00:04:15And there is one more left.
00:04:26Only one right angle in that one and a couple of supplementary.
00:04:29Did you get them, Chris?
00:04:31Yeah.
00:04:32What did you get for angle H?
00:04:34Thirty degrees.
00:04:35Okay, angle H would have to be thirty degrees.
00:04:41Which makes angle J?
00:04:43Thirty degrees.
00:04:43Thirty degrees. Which make angle I?
00:04:48One fifty.
00:04:49One hundred fifty degrees.
00:04:52Why does angle I have to be one fifty?
00:04:55What's the vertical angle...
00:04:59 on the other side? What do we have here?
00:05:03Ninety.
00:05:03Plus?
00:05:04Sixty.
00:05:05Is a hundred and fifty. Therefore ... a hundred and fifty.
00:05:10Okay. Understand those?
00:05:13Yeah.
00:05:13Good. Let's get out the worksheet that I gave earlier in the week and make sure we understand complementary, supplementary, and angle measurements.
00:05:22Crystal.
00:05:23Did you give out a worksheet yesterday-
00:05:24I did not give out a worksheet yesterday. No, we went to the computer lab.
00:05:31You didn't miss anything.
00:05:54Okay, does everybody have worksheet one O three?
00:05:57Yeah.
00:06:00I don't have one.
00:06:05You didn't get worksheet one O- yes, you do. Right there. You got it.
00:06:09I don't know if you had a chance to finish it but if you didn't, I'll give you a chance- to finish it in class today.
00:06:17Okay, what is the complement of an angle of thirty-eight degrees? Tracy?
00:06:27If you didn't get a chance to do it, do it now. Complementary angles add up to what, Tracy?
00:06:33Relax, give- Tracy a chance.
00:06:37Look up at the top definition right here. Complementary angles add up to?
00:06:41Ninety degrees.
00:06:42Ninety degrees. So if I have an angle of thirty-eight degrees...
00:06:46Fifty-two.
00:06:47Thank you, Tracy.
00:06:50If I have an angle of thirty-eight degrees, what is ninety minus thirty-eight?
00:06:55Fifty-two.
00:06:57Fifty-two. So the complement would be fifty-two degrees. Right?
00:07:02What's the complement of an angle of seven degrees? Ho?
00:07:05Eighty-three.
00:07:06Eighty-three.
00:07:07The complement of an angle of eighty-four, Lindsey...
00:07:11Sixteen.
00:07:12You sure about your arithmetic on that one?
00:07:16Six?
00:07:18Six. Six degrees. Alba, number four.
00:07:21Seventy-nine degrees.
00:07:24Number five. Joey?
00:07:26Thirty-three.
00:07:28Sure about that? Claudia?
00:07:30Twenty-
00:07:30Twenty-three. Gotta be careful with the arithmetic. Number six.
00:07:35Jamie.
00:07:36Sixty-one degrees.
00:07:38Good. Number seven. Veronica.
00:07:42Thirty-seven.
00:07:43Thirty-seven. Number eight. Crystal.
00:07:47Forty-four degrees.
00:07:47Forty-four is good. Number nine. That is a tough one. Meryl.
00:07:51Eighty-nine.
00:07:52All right. Number ten.
00:07:55Ho.
00:07:56Thirty-eight.
00:07:57Is there an angle on the page that is supp- complementary to angle ten?
00:08:03Is there another one on that page that was supp- complementary to that angle? Julie.
00:08:09Number one.
00:08:09Number one. Number one and number ten are complementary. How about num- number eleven. That's another tough one. Mike.
00:08:17How much?
00:08:18Forty-five.
00:08:19Good and number twelve.
00:08:21Somebody that hasn't answered yet. Juan.
00:08:24Seventeen.
00:08:25Seventeen degrees. Okay.
00:08:27What about these supplementary angles. They have to add up to what?
00:08:30One eighty.
00:08:32One eighty, right? Okay. Eric, what did you get for number thirteen?
00:08:37One seventy-eight.
00:08:38One seventy-eight. Good. Who hasn't answered yet. Hussein.
00:08:41Did you do number fourteen?
00:08:42No.
00:08:43Okay, John Wolt. Number fourteen.
00:08:46Seventy-nine.
00:08:47Seventy-nine. Okay, Michelle, number fifteen.
00:08:52Eighty-eight.
00:08:52Eighty-eight. If you haven't had a chance to do them, you can do them right now. Number sixteen.
00:08:59Danielle.
00:09:03Check your arithmetic. Okay, it's one eighty minus eighty-two. Carrie.
00:09:08Ninety-eight.
00:09:09Ninety-eight degrees. Number seventeen.
00:09:13Who hasn't answered yet? Angelica, did you do number seventeen?
00:09:17Am I picking on you, dear? I'm sorry.
00:09:19A hundred and sixty-five.
00:09:20A hundred and sixty-five. Perfect. Number eighteen.
00:09:26Patricia.
00:09:27One forty-five. One forty-five.
00:09:29Number eighteen, a hundred and forty-five is a little high.
00:09:35Forty-five.
00:09:36Forty-five. That will work. Number nineteen.
00:09:41Alba.
00:09:43A hundred and thirty-six.
00:09:44A hundred and thirty-six. Number twenty.
00:09:47Arelia.
00:09:49Thirty-one.
00:09:50Thirty-one. Number twenty-one. John.
00:09:54Twelve.
00:09:55Twelve degrees. Number twenty-two. Do we get everybody? Mike.
00:09:59Six degrees.
00:10:00Six degrees. Carlos, number twenty-three.
00:10:04Hundred twenty-one.
00:10:04One twenty-one. And last but not least, a real tough one. Go ahead, Maryl.
00:10:09One.
00:10:10One degree. All right.
00:10:12Did we do the angle measures on the back?
00:10:15Yeah.
00:10:18Except that one. I'll go over that one. Some people had trouble with that.
00:10:22Okay. First of all, before you find the measure of each angle, tell me is angle one acute, obtuse, right, straight? What kind of an angle is it? Julie?
00:10:32Acute?
00:10:32It's an acute angle. I measured it at fourteen degrees.
00:10:38How many people got fourteen degrees plus or minus a couple because I know your protractors.
00:10:43Anybody off by more than two or three degrees on that?
00:10:48Okay, number two. Is that right, acute, obtuse?
00:10:52Acute.
00:10:54Carlos, it's also an acute angle.
00:10:56I measured it at forty-one degrees. How many people got somewhere around there? Forty-one plus or minus?
00:11:04I got forty-seven.
00:11:05Forty-seven?
00:11:07Your protractor is a little more inaccurate than mine are.
00:11:10Okay, I know you don't like these protractors but- you use these because I want everybody to use the same one.
00:11:18Number three, what kind of an angle?
00:11:21Obtuse.
00:11:21Obtuse and I measured it at one hundred fifty-four degrees.
00:11:26Fifty-five.
00:11:28Right around. You know I am gonna give you plus or minus five degrees on a quiz, so don't worry about it.
00:11:37What is the complement of a forty-degree angle?
00:11:42Carlos?
00:11:43Fifty.
00:11:44Would be fifty degrees.
00:11:45What is the complement of a eighty-three-degree angle?
00:11:48Alba?
00:11:49Seven degrees.
00:11:50Seven degrees. Jamie, what about the complement of a sixteen-degree angle?
00:11:54Eighty-four?
00:11:57Seventy-four.
00:11:58Seventy-four. Okay. The supplement of a seventy-five-degree angle. Ho.
00:12:04One O five.
00:12:06Supplement of a hundred and thirty-degree angle. Joey.
00:12:11I didn't do it.
00:12:12Veronica.
00:12:14Fifty degrees.
00:12:14And the supplement of a five-degree angle?
00:12:18Danielle?
00:12:19One seventy-five.
00:12:20One seventy-five. Very good. Let me put the diagram up from...
00:12:24the last three problems...
00:12:27and we'll go over congruency.
00:12:35First of all...
00:12:44This symbol, an equal sign with a little squiggle over the top, means congruent, identically equal to.
00:12:52How many of you remember that symbol and that word from seventh grade?
00:12:57You should have gone over it. Good. What this is saying...
00:13:01and I'll try to draw it as accurately as I can.
00:13:05I have a triangle here...
00:13:10I have another triangle here...
00:13:17and these triangles are labeled A, B, C, N, P, and M.
00:13:26And they are congruent. The symbol for triangle is triangle ABC is congruent to triangle MNP.
00:13:37What is that telling me that they are congruent. What does that mean?
00:13:41Carrie?
00:13:42That they are the same?
00:13:43They are exactly the same triangles.
00:13:47They don't look the same, do they?
00:13:50No.
00:13:50But what can I do to the bottom triangle? I can flip it over, can't I?
00:13:55Yeah.
00:13:55If I had a mirror right here and I just flip that triangle over the mirror, triangle MNP would fit exactly on ABC.
00:14:05So, angle-
00:14:08angle A...
00:14:12would be congruent to which angle in the bottom triangle?
00:14:15Angle M.
00:14:16Veronica?
00:14:17Angle M.
00:14:17Angle M.
00:14:20Line segment.
00:14:24NP.
00:14:25Would be congruent with which line segment in the bottom triangle.
00:14:29Carrie?
00:14:30NP.
00:14:31NP.
00:14:32Remember the symbol for line segment.
00:14:36Okay Carlos, Angle C would be congruent to which angle?
00:14:40P.
00:14:40Would be congruent to angle P, and the last line segment that I think they give us is AC is gonna be congruent with?
00:14:50Joey?
00:14:50MP.
00:14:51MP.
00:14:55Line segment. Okay, everybody got that?
00:14:59No problems.
00:15:01No.
00:15:01All right, I'm gonna give out your worksheet...
00:15:04based on these kind of angles and let you get started on it.
00:15:14Will we need a protractor?
00:15:16You will not need a protractor. This is gonna be by observation. Just like the warm-up.
00:15:45All right. Extra.
00:15:48Okay. When you get the worksheet, let's look at the example on the top. These are very similar-
00:15:54You didn't get one?
00:15:55We need two more.
00:15:55We need two more. Okay.
00:16:03All right, look at the examples on the top.
00:16:06Similar to your warm-up. Look at the figure on the right...
00:16:10and find the measure of each angle.
00:16:13If angle three is one hundred twenty degrees...
00:16:17and angle three and angle one are vertical, what must angle one be equal to?
00:16:24One hundred twenty.
00:16:25One hundred twenty degrees.
00:16:27What can you tell me about angles two and three.
00:16:33They are vertical.
00:16:34Two and three are not vertical.
00:16:37One and three are vertical. Two and four are vertical.
00:16:42Two and three are supplementary.
00:16:44So if three is a hundred and twenty, what must two be equal to?
00:16:49Sixty?
00:16:49Sixty. If two is sixty, what must four be equal to?
00:16:54Sixty.
00:16:55Okay.
00:17:00All the rest are done the same way.
00:17:02Any questions? I'm curious to see, when you get down to number thirty-seven and thirty-eight, you're gonna have to think a little bit.
00:17:09Curious to see what you can come up with on those.
00:17:12You do not need a protractor. This is all by observation.
00:17:52Check your arithmetic.
00:17:58Okay. Seven is eighteen that makes five eighteen, right? What do five and six have to add up to?
00:18:11One hundred eighty.
00:18:12One eighty.
00:18:13So one eighty, minus eighteen would be how much?
00:18:17Ninety-two?
00:18:18Oh no.
00:18:20Just try your subtraction. Okay?
00:18:27Check your arithmetic here.
00:18:31You're right. Five is eighteen degrees. Five and six must add up to what?
00:18:38One eighty.
00:18:39Eighteen plus one seventy-eight. Does that give you one eighty?
00:18:42Oh yeah.
00:18:44Be careful with arithmetic, ladies and gentlemen.
00:18:53Eighteen. One sixty two. One eighty. Perfect.
00:18:56Okay, you're right. Has to be eighteen degrees.
00:19:01What do these- five and six must add up to what number?
00:19:08A hundred and eighty.
00:19:10So if one is eighteen, what is the other one gonna be?
00:19:15One eighty, take away eighteen.
00:19:17Do it- You can do it down here. Do your subtraction.
00:19:21Don't be afraid to have to do subtraction by hand.
00:19:27You sure about this?
00:19:34One eighty minus eighteen.
00:19:36Is only sixty two? Well I'd love to do business with you.
00:19:39Oh.
00:19:41Okay. Number eight- okay. Angle seven is eighteen degrees.
00:19:46Okay, what does angle five have to be?
00:19:48Eighteen degrees.
00:19:49That's right. Okay.
00:19:52And if angle five is eighteen, what does angle- five and six must add up to?
00:20:04A hundred and eighty?
00:20:05So if one's eighteen, what is the other one have to be? What's left?
00:20:09One hundred eighty minus eighteen.
00:20:15Do it. You can do a subtraction here.
00:20:19Okay. You're right- But six and eight are what kind of angles?
00:20:24Supplementary.
00:20:29Oh, vertical angles.
00:20:30And vertical angles are?
00:20:32Hundred and twenty.
00:20:33No. Yeah. Vertical angles are equal.
00:20:37So if six is one sixty-two, eight must also be one sixty-two.
00:20:43Vertical angles must be equal.
00:20:44Oh. All right.
00:20:46Okay?
00:20:47Okay. I know that one and that one are both eighteen degrees
00:20:51and I know that one is one sixty-two 'cause that one is eighteen so would that be one sixty-two?
00:20:57Exactly. 'Cause they're vertical angles and they must be equal.
00:21:00Remember, when you intersect lines, there are two sets of vertical angles.
00:21:06Is this right?
00:21:07No.
00:21:09Okay.
00:21:10I don't understand how to do this.
00:21:12One sixty.
00:21:13Yeah- just check your arithmetic. I lost my pencil.
00:21:16Okay, you know this is eighteen, so this is eighteen, right?
00:21:20If this is eighteen, five and six are a straight angle.
00:21:24What must they add up to?
00:21:28They're supplementary.
00:21:31One eighty?
00:21:32Okay, so one eighty minus the eighteen you already have...
00:21:38gives you one sixty-two.
00:21:39Oh okay.
00:21:40And if this is one sixty- two, then this one must also be... what?
00:21:44One sixty-two.
00:21:45Very good.
00:21:46How would you do this one?
00:21:48Okay, number nine is sixty-three, number eleven is sixty-three. Same way.
00:21:52Okay.
00:21:53Okay. If nine is sixty-three, ten must be one eighty minus sixty-three...
00:21:59Oh okay, I see.
00:22:01and then twelve would be the same as ten.
00:22:02Oh okay. Okay, thank you. Thanks.
00:22:04So then number ten would be? Oh.
00:22:07Ten would have to be one seventeen?
00:22:09Yeah.
00:22:11Thanks, Mr. Thuma.
00:22:12I understand how to do all of this,
00:22:13but I'm not sure what they're asking on number thirty-seven.
00:22:20It's says that there is an angle that has exactly the same measure as its supplement.
00:22:27So it's like the one before?
00:22:29Think about it. Just think a minute.
00:22:31You have two angles that are supplementary which add up to what?
00:22:36One eighty.
00:22:36One eighty. And they're both the same.
00:22:40So they're ninety-degree angles.
00:22:41There you go.
00:22:42Mr. Thuma, what are the- letters for?
00:22:45Don't worry about the letters; that's just identifying points.
00:22:49Remember these are lines. This is line HJ.
00:22:52It's not asking anything about the lines just about the angles.
00:22:59You have a hundred and thirty-six here. Fourteen. What must sixteen be equal to?
00:23:07They're vertical angles. Vertical angles are always ... equal.
00:23:12And fourteen and fifteen must add up to one eighty.
00:23:17Right? They're all the same. These are supplementary. They must add up to one eighty. These are equal.
00:23:23All right.
00:23:25That one.
00:23:29You sure about that?
00:23:30That means one angle is sixty and the supplement would be a hundred and twenty which is not the same measure.
00:23:37Think about it. I'll help you with thirty si-... Yes, that's right.
00:23:44Think about on thirty-seven and thirty-eight. You must really give these problems a little bit of thought, but don't give up on them.
00:23:54I don't get this- Write an equation that represents the sentence, the product-
00:23:57Think about it. What does product mean?
00:24:02Sum means...
00:24:06Let's go over some definitions. Sum means to do what?
00:24:09Add.
00:24:09If I said find the sum. If I said find the difference?
00:24:14Subtract.
00:24:17What does the word product tell you to do?
00:24:25Product is a multiplication problem.
00:24:34Wouldn't you add both of these.
00:24:39No, no. You would add this and this.
00:24:41But if it's-
00:24:42And it's gotta add up to one eighty.
00:24:44But if it's all one big angle wouldn't you add both of them?
00:24:49If you add up all four, you should get three sixty.
00:24:52Is that how it is supposed to be?
00:24:54Yeah, the total should be three sixty. And your arithmetic is off a little bit here.
00:24:57Okay.
00:25:02Is this-
00:25:03Okay, I'm gonna- go over it in a few minutes.
00:25:08No, no, no, no.
00:25:10It says an angle has the same measure as its supplement.
00:25:14That means the two of them, the two angles add up to how much?
00:25:19Hundred eighty.
00:25:21And each one is exactly the same.
00:25:28Think about it.
00:25:30What are two angles that are exactly the same that add up to one eighty?
00:25:38It is one sixty-two?
00:25:39Yes. Yes.
00:25:41How come you told me that it was wrong when I answered the first time?
00:25:47That was what I had the first time and you said it was wrong.
00:25:49No, no.
00:25:50I thought you had sixty-two.
00:25:52No, you had an eight at the end. There was an eight there some place. One seventy-eight or something like that.
00:26:03Okay, do you have the attendance? Did you bubble it?
00:26:07What do you mean which is angle QRS?
00:26:08Well, where is it?
00:26:17Oh, those are- Yes. Somebody came in first period and got them. Thanks.
00:26:30I don't wanna give it away.
00:26:32It is ninety?
00:26:33It's gotta be. Think about it.
00:26:37Look at problem thirty-seven.
00:26:40Two angles are supplementary.
00:26:42Therefore, they must add up to a hundred eighty degrees but they are...
00:26:48 equal, so let's call one QRS and the other one SRT.
00:26:54Each one of them's gotta be...
00:26:56Ninety.
00:26:57...a ninety degree angle.
00:27:00That's the only way.
00:27:04Do you have a question, Mike?
00:27:09You got it.
00:27:11And we had it before you wrote it on the board.
00:27:14Yes. S cannot be over there. QRS.
00:27:20R must be the vertex. R must be the vertex.
00:27:23Where did you get the T from?
00:27:25I just made that up. It just says as it's supplement.
00:27:29I called the supplement SRT. I just added the next logical letter, right?
00:27:42Where is he going?
00:27:43To the bathroom.
00:27:44Take the wooden pass.
00:27:49Okay.
00:27:51Has anyone- you had a question, Carrie?
00:27:55All right. How-
00:27:59Jay Ho, you can put your cereal box away right now. I know everybody's got that project.
00:28:04Yeah, Ho. Put your cereal box away.
00:28:06Has ...
00:28:08anyone come up, knowing that the product means multiplication?
00:28:13Has anyone come up with the answer to number thirty-eight?
00:28:18What?
00:28:19Yes.
00:28:21No.
00:28:24What did you get, Danielle?
00:28:28No. No, thirty-eight. It says write an equation that represents the sentence, the product of twelve and a number is one ninety-two.
00:28:38Is it twelve K?
00:28:41Twelve K?
00:28:42Twelve and the number K- twelve K...
00:28:47is one ninety-two.
00:28:50Equal sign.
00:28:53Excellent.
00:28:54That's it?
00:28:55That's it. Twelve- doesn't it say the product of twelve and the number K is one hundred ninety-two.
00:29:04Remember, a math equation is just a sentence written with symbols.
00:29:11How many people need a few more minutes on this worksheet?
00:29:14I don't get number thirty-seven.
00:29:17Thirty-seven is ninety degrees.
00:29:18Thirty-seven is two ninety-degree angles.
00:29:21Cool.
00:29:21An angle and it's supplement are the same. They must add up to one eighty...
00:29:27and they're the same.
00:29:28Two ninety degrees?
00:29:30So what is the measure of the angle? The measure of the angle has to be ninety degrees.
00:29:36Right?
00:29:45You can do those last two.
00:29:47Which one? Those-
00:29:49Thirty-nine to forty.
00:30:00Finished.
00:30:01Finished.
00:30:02Okay, you need to measure these.
00:30:06Good.
00:30:19We have time to go over the worksheet from Friday.
00:30:26All right. How many people need a couple extra minutes on this? Carrie, question?
00:30:35Thirty-nine? I know we did integers a couple months ago but come on.
00:30:40I know but I forgot.
00:30:43A negative...
00:30:47No, no, no. Time out.
00:30:51This-
00:30:55I'll answer as soon as everybody is listening. You got confused when I went from addition to multiplication.
00:31:04A negative plus a negative must be?
00:31:09Positive.
00:31:09Negative.
00:31:10Why?
00:31:12A negative times a negative is positive.
00:31:15Okay.
00:31:16But if I take twenty-six steps backwards ... and then I take another twenty-eight steps backwards, I'm not gonna wind up going forwards, am I?
00:31:25No.
00:31:26No. Danielle.
00:31:28Is number forty-seven, seven?
00:31:29That's correct. The complement of an eighty-three degree angle must be seven.
00:31:36All right.
00:31:39The worksheet we did on Friday after the quiz... we can go over that too today.
00:31:46I don't understand that.
00:31:47You didn't get one, Pat?
00:31:52After the quiz Friday. You didn't pick one up?
00:31:59Were we supposed to-
00:32:01No, but a lot of people did which is why I ran out of copies. This was only supposed to be a class set.
00:32:11Is number forty, seven degrees?
00:32:13Number forty should be seven degrees. Right.
00:32:16I didn't get one.
00:32:16You weren't here Friday?
00:32:22What are we doing tomorrow?
00:32:23Tomorrow, I am going to review everything on angles ...
00:32:28and you're gonna have a quiz on Friday which will be on complementary, supplementary, vertical, all of the stuff that we did today, okay?
00:32:44All right. On Friday after the quiz, I asked you to pick up worksheets exercises fifteen and thirty-five... They should be on a separate sheet of paper.
00:32:56Except for the couple of people, I just gave a copy to- let's take a look at them.
00:33:01I didn't do them.
00:33:03After the quiz on Friday.
00:33:06Didn't have time. I didn't do it.
00:33:08I did it. I finished.
00:33:11Things have improved. Haven't they, Meryl?
00:33:18You should have a separate sheet of paper with your answers on it. Yeah.
00:33:23There was only a class set of these, although some people did walk off with them.
00:33:32All right, exercise fifteen asked you ...
00:33:38what was the angle that First Street makes with Main Street?
00:33:43Forty-five.
00:33:45It was a forty-five- degree angle.
00:33:49What is the angle that the property line between the two lots- and the property line ... you have the two lots A and B...
00:34:02Here is Main ... Here is First.
00:34:06I haven't drawn it exact but ... what was the property line-
00:34:12the angle that the property line made with First Street?
00:34:16Now some of you may have measured the acute angle. Some of you may also have measured the...
00:34:23Obtuse.
00:34:24Obtuse angle. What did you get for that angle?
00:34:26For the obtuse angle I got one thirty-four.
00:34:28Okay, so you measured the obtuse angle. Okay? Which came out to?
00:34:35Actually, let's round it off because I think it was supposed to be drawn as an isosceles triangle. Okay?
00:34:43So we round this off to one thirty-five. We've got forty-five here. This also should have been a forty-five degree angle in here,
00:34:50give or take a degree or two.
00:34:54What is the angle that the property line between the two lots makes with Main Street? That was handed to you.
00:35:02Right, Lindsey? It should have been ninety degrees, right?
00:35:06Could you suggest a more equal way-
00:35:09If I had a piece of property...
00:35:13triangular like this...
00:35:16is this an even way to divide it if I take the midpoint here to the midpoint here, is that giving two equal size lots?
00:35:24No.
00:35:24Joey, how would you divide it up to make it equal?
00:35:27From the middle of First Street...
00:35:30From the middle of First Street...
00:35:32...down to the corner of the-
00:35:33...down to the corner over here. Now my drawing is not exactly accurate, but that would give you two equal pieces of property out of the same triangle.
00:35:46All right, on exercise thirty-five...
00:35:51How many of you were able to measure those angles and come up very close to seven hundred twenty degrees... within say five?
00:36:05That's all? Only a couple of you? Carrie, how far off were you when you added them up?
00:36:14It's a six-sided piece of property- one, two, three, four-
00:36:18There are six sides.
00:36:24The sum of the angles should be seven hundred twenty degrees.
00:36:34What did you get as a total. John?
00:36:38Seventy-two.
00:36:42Only seventy-two degrees for the six angles?
00:36:45Seven eighteen.
00:36:47Seven eighteen.
00:36:48Oh. Seven eighteen. That's pretty darn close. Within five degrees. How many got seven twenty? Within five degrees.
00:36:55Okay.
00:36:56I got seven twenty exactly.
00:36:58Seven twenty exactly. You were accurate with your protractor. If I move that bottom angle...
00:37:08started out like this, let me see if I can recreate it here for you.
00:37:13One was here, then the line came down here, then went back here. One, two, three, four- this is about what it looked like.
00:37:20This was B, A, F, E, D, and C.
00:37:29If I took ... this angle ...
00:37:34and moved it ... down here ...
00:37:39and made it across this way, moved D down here, should that change the sum- the total of my-
00:37:47Angles?
00:37:47No.
00:37:48It should not. Why? I still have how many angles? Joey.
00:37:53You still have six.
00:37:54I still have six angles.
00:37:57There is a formula and we are gonna go through this after spring break, but I am gonna give you a hint right now.
00:38:04If I take the number of sides ...
00:38:10and I subtract two ...
00:38:14and I multiply that number times one hundred eighty degrees ...
00:38:21that will tell me how many degrees these add up to.
00:38:25How many sides in this figure?
00:38:27Six.
00:38:29How many sides?
00:38:30How many sides in this figure? One, two, three, four, five, six, right? Number of sides, subtract two.
00:38:39Gives me what?
00:38:40Four.
00:38:40Four. What is four times one hundred eighty degrees?
00:38:47Seven hundred twenty.
00:38:48Should be seven hundred twenty, right? How many ... how many degrees should there be in a five-sided figure?
00:38:58A pentagon.
00:39:02Take the formula. Number of sides is five. You don't have to do it in your head. You have pencil and paper.
00:39:13Number of sides is five...
00:39:16Subtract two, and multiply it by one hundred eighty degrees.
00:39:21Five hundred and forty degrees.
00:39:23All five-sided figures contain five hundred forty degrees.
00:39:31Triangle has how many sides?
00:39:33Three.
00:39:33Take away two is one; one times one eighty.
00:39:36A triangle contains eighty degrees.
00:39:39Wouldn't it be one eighty?
00:39:40One hundred eighty degrees. Thank you, Liz. A square. Four sides or rectangle, subtract two is two times one eighty. Three hundred sixty degrees.
00:39:52You can always figure out the total number of degrees in a figure by taking the number of sides, subtracting two, and multiplying by one eighty.
00:40:07How many degrees in a triangle?
00:40:09SOne eighty.
00:40:10One eighty... What is an equilateral triangle?
00:40:15Equal on all sides.
00:40:16Equal on all sides. If an equilateral triangle is equal on all sides,
00:40:22how many degrees are in each angle of an equilateral triangle? Carlos.
00:40:29Sixty.
00:40:30Sixty. It's gotta be sixty, sixty, and sixty. What is an isosceles triangle?
00:40:36It's what we are gonna do tomorrow but we are getting a head start on it. Joey?
00:40:39Two of the angles are the same.
00:40:42Two angles are the same and two...
00:40:46Sides.
00:40:47sides are both the same. An isosceles triangle has two equal sides, therefore two equal angles. What is a scalene triangle? Who remembers the word scalene. Crystal?
00:40:59A triangle that doesn't have any of the sides that are the same.
00:41:02None of the sides are equal, right?
00:41:10Tomorrow we are gonna go over triangles ... Friday, tomorrow I will introduce triangles.
00:41:16We're gonna review for the quiz.
00:41:17Your quiz on Friday will contain complementary angles, supplementary angles, vertical angles, and that's about it. Next week...
00:41:28Next week, we're gonna finish this unit.
00:41:32I wanna finish the unit- let me finish and then you can ask- or tell me who is going on vacation early or what.
00:41:39Next week, I want to finish the unit because I don't wanna continue the unit past spring break.
00:41:45The unit test next week will be on Thursday.
00:41:50Because I am afraid some of you may be leaving early for vacation and will not be here on Friday.
00:41:55So if you're not here on Thursday, we'll have to give you a make up when you come back. I can't give it any earlier. Okay, Veronica.
00:42:04But if you're gonna explain it tomorrow, what about the people that are going to Knotts?
00:42:09I am not going to go into any great det- I basically explained to you ... what's going on with trianglescalene, equilateral, isosceles.
00:42:21Just an introduction.
00:42:24The thing you'll miss the most if you're going to Knotts tomorrow is this review which I have already pretty much given you today. Okay?
00:42:32Claudia, two supplementary angles add up to how many degrees? Supplementary.
00:42:38One eighty.
00:42:39One eighty. How can you remember supplementary and complementary and what they add up to? Veronica.
00:42:47Because supplementary- S comes last after C.
00:42:53C comes before S in the alphabet. Ninety comes before one eighty in numbers. Complementary: ninety. Supplementary: one eighty.
00:43:03What can you tell me about vertical angles?
00:43:07Eric.
00:43:08That they're a hundred and eighty.
00:43:10Vertical angles do not necessarily have to be one eighty.
00:43:17Vertical angles must be...
00:43:21Say it, John. Equal. Vertical angles are equal.
00:43:26They must be equal. What is a straight angle?
00:43:29SOne eighty.
00:43:31A right angle.
00:43:33SNinety.
00:43:34An acute angle?
00:43:35SLess than ninety.
00:43:37Less than ninety, greater than zero. Straight angle?
00:43:42SOne eighty.
00:43:44One eighty. Reflex angle?
00:43:48I know. More than one eighty.
00:43:49More than one eighty. How is that possible?
00:43:52It's a circle.
00:43:52If you measure around the opposite way.
00:44:02I can measure this angle two ways. I can measure the inside which would be obtuse,
00:44:08or I can measure it around the outside. That would make this a reflex angle greater than one hundred eighty degrees.
00:44:17Okay, Alba, you had a comment or question you wanted to make before?
00:44:20It was the same one.
00:44:21It was the same one. Okay, how many people are going to Knotts tomorrow?
00:44:25Oh gosh, I'm gonna have a day off.
00:44:28Congratulations. Proud of you. The Knotts Berry Farm trip for all what? Five O's or six O's.
00:44:35And you didn't give me an O either.
00:44:38No, Maryl, I didn't- and you're going?
00:44:41I'm the only one that didn't give you an O?
00:44:43Just kiddin'.
00:44:44Oh okay. All right, we've got about four minutes to the bell. If you need to finish up any of this ... ask me any questions...
00:45:03Did you get everything you need from it, Danielle?
00:45:05Yeah.
00:45:06Thank you.
00:45:15Okay. You getting this?
00:45:16Yeah.
00:45:17Let me see. Let me see your worksheet.
00:45:22Okay, you got these. Good.
00:45:23I don't get this.
00:45:25Product means multiplication.
00:45:29K is a variable. Remember? The product of twelve ... and a number that's multiplication is...
00:45:40one ninety-two.
00:45:44And a negative plus a negative has to be negative, so this is negative fifty-four. Okay?
00:46:00You can stay in your seat until the bell rings.
00:46:04All done with this, Pat?
00:46:13The quiz Friday will cover no more than we've done- there will be no new information tomorrow for the quiz on Friday. Okay?
00:46:23The next worksheet will not be until Friday after the quiz and it's- it's gonna be on triangles. Carrie.
00:46:33Tomorrow. Yeah, I'll answer all questions tomorrow on angles. I will make sure you understand 'em.
00:46:39So if you understand them- Are you going to Knotts?
00:46:43I got six O's but-
00:46:45But you're not going. Your choice.
00:46:58What school did you come from, Carlos?
00:47:00Inland, right?
00:47:03So you had pretty much all of this before you transferred. Were you an A student in math before you got here?
00:47:09Yeah.
00:47:10Were you? Seems to be. Excuse me, Maryl.
00:47:14I was throwing her back her cereal box.
00:47:15Why can't you hand her back her cereal box? This isn't sixth period.
00:47:20It flies so nice.
00:47:22I said because it flies-
00:47:23It flies so nice. Really nice.
00:47:28I think we have an announcement coming.
00:47:30O: There is an informational meeting today during nutrition, in the lyceum, for all freshmen interested in joining the Vincent Academy next year.
00:47:41It's not you.
00:47:44Freshmen. You- wanna start your high school career over again?
00:47:46...freshmen, interested in joining the Vincent Academy. Please be on time. Thank you.
00:47:58Okay, you've got about half a minute. If you'd like to line up by the door, you may.
00:48:14Have a good day.
00:48:16Thank you, Jamie. You too.
00:48:20We have no class tomorrow.
00:48:21It's gonna be nice. Five, four, three, two, one, [Bell] bye.
00:48:30SBye, Mr. Thuma.
00:48:31We have to think. All the good people are gonna be gone.
00:48:34That's true. I'm left with the people that don't get the O's.