# US87 (FROM TIMSS 1995 VIDEO STUDY)

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

Time | Caption |
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00:00:02 | What is the angle that is vertical to the seventy-degree angle? |

00:00:07 | Vertical angles are formed by what, Juan? |

00:00:10 | I don't know. I was just stretching. |

00:00:13 | Don't get nervous. He's just stretching. |

00:00:15 | When 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. |

00:00:27 | Here we have vertical angles and supplementary angles. |

00:00:30 | Angle A is vertical to which angle? |

00:00:34 | Seventy. |

00:00:35 | Therefore angle A must be... |

00:00:38 | Seventy. |

00:00:38 | Seventy degrees. Go from there. Now you have supplementary angles, don't you? |

00:00:44 | What angle is supplementary to angle B? |

00:00:48 | A. |

00:00:49 | I mean, I'm sorry. Angle A. |

00:00:50 | B. |

00:00:51 | B is and so is? |

00:00:52 | S//C. |

00:00:52 | //C. Supplementary angles add up to what number? |

00:00:58 | One eighty. |

00:00:59 | One hundred eighty degrees. So if you know one is seventy, |

00:01:02 | the other one has to be? |

00:01:04 | Hundred ten. |

00:01:04 | A hundred ten. Go from there. |

00:01:06 | Okay, you have all your information, |

00:01:09 | so we already figured these out. |

00:01:11 | We have the measure of angle A is seventy degrees. |

00:01:15 | B is a hundred ten and C is a hundred and ten. We know that. |

00:01:21 | What information are we given in the second problem for D? |

00:01:25 | Fifty-three degrees. |

00:01:27 | Okay. Two things. You have fifty-three degrees. |

00:01:31 | What is the other angle I've indicated in there? |

00:01:34 | Mike? |

00:01:35 | Right angle. |

00:01:36 | It's a right angle which add up to? |

00:01:37 | Ninety. |

00:01:37 | Ninety degrees. Okay? |

00:01:40 | What's left? |

00:01:43 | Somebody just gave me the answer. |

00:01:45 | Thirty-seven. |

00:01:45 | Thirty-seven degrees, right? |

00:01:50 | Why thirty-seven degrees, Jamie? |

00:01:54 | Carrie? |

00:01:55 | Because thirty-seven and fifty-three equals ninety. |

00:01:59 | Thirty-seven and fifty-three equals ninety. The middle angle is ninety |

00:02:02 | and why did they all have to add up to one eighty? |

00:02:05 | Because it's- it's a- |

00:02:07 | Because it's a? Veronica. |

00:02:10 | What is this angle called here? |

00:02:12 | A straight. |

00:02:13 | A straight angle. And a straight angle adds up to? |

00:02:15 | One eighty. |

00:02:15 | One eighty. |

00:02:16 | Okay, you think, in a couple of minutes, you can figure out the rest of them? |

00:02:20 | I think so. |

00:02:33 | Is E, F, and G a bit confusing? |

00:02:35 | How many right angles do you see in that- |

00:02:37 | Two. |

00:02:38 | There are two right angles, right? |

00:02:40 | Yeah. |

00:02:40 | Okay. |

00:03:00 | Okay, you want some prompting on this one? |

00:03:03 | Question? Carrie, what? |

00:03:06 | I don't understand which one's you're supposed to- |

00:03:08 | Which ones are the right angles? |

00:03:08 | Yeah. |

00:03:09 | Okay, I have a right angle here... |

00:03:13 | This angle right here is a right angle... |

00:03:16 | and this angle here- I should of used colored chalk. |

00:03:19 | This angle here is a right angle. Okay. |

00:03:22 | So work backwards. |

00:03:23 | If this angle here is a right angle and this is thirty degrees, |

00:03:26 | what does G have to be? |

00:03:28 | Sixty? |

00:03:28 | G has to be? |

00:03:30 | Sixty. |

00:03:30 | Sixty. Okay? |

00:03:37 | If this angle is also a right angle in here and this is thirty, |

00:03:41 | what does F have to be? |

00:03:42 | Sixty. |

00:03:43 | Sixty. |

00:03:45 | And what's left then for angle E? |

00:03:50 | Thirty. |

00:03:51 | They all have to add up to? |

00:03:54 | Okay, so if we have a sixty-degree angle and this- |

00:03:58 | If this angle is a right angle ... what about this on the other side? |

00:04:03 | That also has to be a right angle, doesn't it? |

00:04:06 | Yeah. |

00:04:07 | Because ninety plus ninety is? |

00:04:09 | A hundred eight- |

00:04:09 | One eighty. So what we have left for E is another thirty-degree angle. |

00:04:15 | And there is one more left. |

00:04:26 | Only one right angle in that one and a couple of supplementary. |

00:04:29 | Did you get them, Chris? |

00:04:31 | Yeah. |

00:04:32 | What did you get for angle H? |

00:04:34 | Thirty degrees. |

00:04:35 | Okay, angle H would have to be thirty degrees. |

00:04:41 | Which makes angle J? |

00:04:43 | Thirty degrees. |

00:04:43 | Thirty degrees. Which make angle I? |

00:04:48 | One fifty. |

00:04:49 | One hundred fifty degrees. |

00:04:52 | Why does angle I have to be one fifty? |

00:04:55 | What's the vertical angle... |

00:04:59 | on the other side? What do we have here? |

00:05:03 | Ninety. |

00:05:03 | Plus? |

00:05:04 | Sixty. |

00:05:05 | Is a hundred and fifty. Therefore ... a hundred and fifty. |

00:05:10 | Okay. Understand those? |

00:05:13 | Yeah. |

00:05:13 | Good. Let's get out the worksheet that I gave earlier in the week and make sure we understand complementary, supplementary, and angle measurements. |

00:05:22 | Crystal. |

00:05:23 | Did you give out a worksheet yesterday- |

00:05:24 | I did not give out a worksheet yesterday. No, we went to the computer lab. |

00:05:31 | You didn't miss anything. |

00:05:54 | Okay, does everybody have worksheet one O three? |

00:05:57 | Yeah. |

00:06:00 | I don't have one. |

00:06:05 | You didn't get worksheet one O- yes, you do. Right there. You got it. |

00:06:09 | I 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. |

00:06:17 | Okay, what is the complement of an angle of thirty-eight degrees? Tracy? |

00:06:27 | If you didn't get a chance to do it, do it now. Complementary angles add up to what, Tracy? |

00:06:33 | Relax, give- Tracy a chance. |

00:06:37 | Look up at the top definition right here. Complementary angles add up to? |

00:06:41 | Ninety degrees. |

00:06:42 | Ninety degrees. So if I have an angle of thirty-eight degrees... |

00:06:46 | Fifty-two. |

00:06:47 | Thank you, Tracy. |

00:06:50 | If I have an angle of thirty-eight degrees, what is ninety minus thirty-eight? |

00:06:55 | Fifty-two. |

00:06:57 | Fifty-two. So the complement would be fifty-two degrees. Right? |

00:07:02 | What's the complement of an angle of seven degrees? Ho? |

00:07:05 | Eighty-three. |

00:07:06 | Eighty-three. |

00:07:07 | The complement of an angle of eighty-four, Lindsey... |

00:07:11 | Sixteen. |

00:07:12 | You sure about your arithmetic on that one? |

00:07:16 | Six? |

00:07:18 | Six. Six degrees. Alba, number four. |

00:07:21 | Seventy-nine degrees. |

00:07:24 | Number five. Joey? |

00:07:26 | Thirty-three. |

00:07:28 | Sure about that? Claudia? |

00:07:30 | Twenty- |

00:07:30 | Twenty-three. Gotta be careful with the arithmetic. Number six. |

00:07:35 | Jamie. |

00:07:36 | Sixty-one degrees. |

00:07:38 | Good. Number seven. Veronica. |

00:07:42 | Thirty-seven. |

00:07:43 | Thirty-seven. Number eight. Crystal. |

00:07:47 | Forty-four degrees. |

00:07:47 | Forty-four is good. Number nine. That is a tough one. Meryl. |

00:07:51 | Eighty-nine. |

00:07:52 | All right. Number ten. |

00:07:55 | Ho. |

00:07:56 | Thirty-eight. |

00:07:57 | Is there an angle on the page that is supp- complementary to angle ten? |

00:08:03 | Is there another one on that page that was supp- complementary to that angle? Julie. |

00:08:09 | Number one. |

00:08:09 | Number one. Number one and number ten are complementary. How about num- number eleven. That's another tough one. Mike. |

00:08:17 | How much? |

00:08:18 | Forty-five. |

00:08:19 | Good and number twelve. |

00:08:21 | Somebody that hasn't answered yet. Juan. |

00:08:24 | Seventeen. |

00:08:25 | Seventeen degrees. Okay. |

00:08:27 | What about these supplementary angles. They have to add up to what? |

00:08:30 | One eighty. |

00:08:32 | One eighty, right? Okay. Eric, what did you get for number thirteen? |

00:08:37 | One seventy-eight. |

00:08:38 | One seventy-eight. Good. Who hasn't answered yet. Hussein. |

00:08:41 | Did you do number fourteen? |

00:08:42 | No. |

00:08:43 | Okay, John Wolt. Number fourteen. |

00:08:46 | Seventy-nine. |

00:08:47 | Seventy-nine. Okay, Michelle, number fifteen. |

00:08:52 | Eighty-eight. |

00:08:52 | Eighty-eight. If you haven't had a chance to do them, you can do them right now. Number sixteen. |

00:08:59 | Danielle. |

00:09:03 | Check your arithmetic. Okay, it's one eighty minus eighty-two. Carrie. |

00:09:08 | Ninety-eight. |

00:09:09 | Ninety-eight degrees. Number seventeen. |

00:09:13 | Who hasn't answered yet? Angelica, did you do number seventeen? |

00:09:17 | Am I picking on you, dear? I'm sorry. |

00:09:19 | A hundred and sixty-five. |

00:09:20 | A hundred and sixty-five. Perfect. Number eighteen. |

00:09:26 | Patricia. |

00:09:27 | One forty-five. One forty-five. |

00:09:29 | Number eighteen, a hundred and forty-five is a little high. |

00:09:35 | Forty-five. |

00:09:36 | Forty-five. That will work. Number nineteen. |

00:09:41 | Alba. |

00:09:43 | A hundred and thirty-six. |

00:09:44 | A hundred and thirty-six. Number twenty. |

00:09:47 | Arelia. |

00:09:49 | Thirty-one. |

00:09:50 | Thirty-one. Number twenty-one. John. |

00:09:54 | Twelve. |

00:09:55 | Twelve degrees. Number twenty-two. Do we get everybody? Mike. |

00:09:59 | Six degrees. |

00:10:00 | Six degrees. Carlos, number twenty-three. |

00:10:04 | Hundred twenty-one. |

00:10:04 | One twenty-one. And last but not least, a real tough one. Go ahead, Maryl. |

00:10:09 | One. |

00:10:10 | One degree. All right. |

00:10:12 | Did we do the angle measures on the back? |

00:10:15 | Yeah. |

00:10:18 | Except that one. I'll go over that one. Some people had trouble with that. |

00:10:22 | Okay. 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? |

00:10:32 | Acute? |

00:10:32 | It's an acute angle. I measured it at fourteen degrees. |

00:10:38 | How many people got fourteen degrees plus or minus a couple because I know your protractors. |

00:10:43 | Anybody off by more than two or three degrees on that? |

00:10:48 | Okay, number two. Is that right, acute, obtuse? |

00:10:52 | Acute. |

00:10:54 | Carlos, it's also an acute angle. |

00:10:56 | I measured it at forty-one degrees. How many people got somewhere around there? Forty-one plus or minus? |

00:11:04 | I got forty-seven. |

00:11:05 | Forty-seven? |

00:11:07 | Your protractor is a little more inaccurate than mine are. |

00:11:10 | Okay, I know you don't like these protractors but- you use these because I want everybody to use the same one. |

00:11:18 | Number three, what kind of an angle? |

00:11:21 | Obtuse. |

00:11:21 | Obtuse and I measured it at one hundred fifty-four degrees. |

00:11:26 | Fifty-five. |

00:11:28 | Right around. You know I am gonna give you plus or minus five degrees on a quiz, so don't worry about it. |

00:11:37 | What is the complement of a forty-degree angle? |

00:11:42 | Carlos? |

00:11:43 | Fifty. |

00:11:44 | Would be fifty degrees. |

00:11:45 | What is the complement of a eighty-three-degree angle? |

00:11:48 | Alba? |

00:11:49 | Seven degrees. |

00:11:50 | Seven degrees. Jamie, what about the complement of a sixteen-degree angle? |

00:11:54 | Eighty-four? |

00:11:57 | Seventy-four. |

00:11:58 | Seventy-four. Okay. The supplement of a seventy-five-degree angle. Ho. |

00:12:04 | One O five. |

00:12:06 | Supplement of a hundred and thirty-degree angle. Joey. |

00:12:11 | I didn't do it. |

00:12:12 | Veronica. |

00:12:14 | Fifty degrees. |

00:12:14 | And the supplement of a five-degree angle? |

00:12:18 | Danielle? |

00:12:19 | One seventy-five. |

00:12:20 | One seventy-five. Very good. Let me put the diagram up from... |

00:12:24 | the last three problems... |

00:12:27 | and we'll go over congruency. |

00:12:35 | First of all... |

00:12:44 | This symbol, an equal sign with a little squiggle over the top, means congruent, identically equal to. |

00:12:52 | How many of you remember that symbol and that word from seventh grade? |

00:12:57 | You should have gone over it. Good. What this is saying... |

00:13:01 | and I'll try to draw it as accurately as I can. |

00:13:05 | I have a triangle here... |

00:13:10 | I have another triangle here... |

00:13:17 | and these triangles are labeled A, B, C, N, P, and M. |

00:13:26 | And they are congruent. The symbol for triangle is triangle ABC is congruent to triangle MNP. |

00:13:37 | What is that telling me that they are congruent. What does that mean? |

00:13:41 | Carrie? |

00:13:42 | That they are the same? |

00:13:43 | They are exactly the same triangles. |

00:13:47 | They don't look the same, do they? |

00:13:50 | No. |

00:13:50 | But what can I do to the bottom triangle? I can flip it over, can't I? |

00:13:55 | Yeah. |

00:13:55 | If I had a mirror right here and I just flip that triangle over the mirror, triangle MNP would fit exactly on ABC. |

00:14:05 | So, angle- |

00:14:08 | angle A... |

00:14:12 | would be congruent to which angle in the bottom triangle? |

00:14:15 | Angle M. |

00:14:16 | Veronica? |

00:14:17 | Angle M. |

00:14:17 | Angle M. |

00:14:20 | Line segment. |

00:14:24 | NP. |

00:14:25 | Would be congruent with which line segment in the bottom triangle. |

00:14:29 | Carrie? |

00:14:30 | NP. |

00:14:31 | NP. |

00:14:32 | Remember the symbol for line segment. |

00:14:36 | Okay Carlos, Angle C would be congruent to which angle? |

00:14:40 | P. |

00:14:40 | Would be congruent to angle P, and the last line segment that I think they give us is AC is gonna be congruent with? |

00:14:50 | Joey? |

00:14:50 | MP. |

00:14:51 | MP. |

00:14:55 | Line segment. Okay, everybody got that? |

00:14:59 | No problems. |

00:15:01 | No. |

00:15:01 | All right, I'm gonna give out your worksheet... |

00:15:04 | based on these kind of angles and let you get started on it. |

00:15:14 | Will we need a protractor? |

00:15:16 | You will not need a protractor. This is gonna be by observation. Just like the warm-up. |

00:15:45 | All right. Extra. |

00:15:48 | Okay. When you get the worksheet, let's look at the example on the top. These are very similar- |

00:15:54 | You didn't get one? |

00:15:55 | We need two more. |

00:15:55 | We need two more. Okay. |

00:16:03 | All right, look at the examples on the top. |

00:16:06 | Similar to your warm-up. Look at the figure on the right... |

00:16:10 | and find the measure of each angle. |

00:16:13 | If angle three is one hundred twenty degrees... |

00:16:17 | and angle three and angle one are vertical, what must angle one be equal to? |

00:16:24 | One hundred twenty. |

00:16:25 | One hundred twenty degrees. |

00:16:27 | What can you tell me about angles two and three. |

00:16:33 | They are vertical. |

00:16:34 | Two and three are not vertical. |

00:16:37 | One and three are vertical. Two and four are vertical. |

00:16:42 | Two and three are supplementary. |

00:16:44 | So if three is a hundred and twenty, what must two be equal to? |

00:16:49 | Sixty? |

00:16:49 | Sixty. If two is sixty, what must four be equal to? |

00:16:54 | Sixty. |

00:16:55 | Okay. |

00:17:00 | All the rest are done the same way. |

00:17:02 | Any 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. |

00:17:09 | Curious to see what you can come up with on those. |

00:17:12 | You do not need a protractor. This is all by observation. |

00:17:52 | Check your arithmetic. |

00:17:58 | Okay. Seven is eighteen that makes five eighteen, right? What do five and six have to add up to? |

00:18:11 | One hundred eighty. |

00:18:12 | One eighty. |

00:18:13 | So one eighty, minus eighteen would be how much? |

00:18:17 | Ninety-two? |

00:18:18 | Oh no. |

00:18:20 | Just try your subtraction. Okay? |

00:18:27 | Check your arithmetic here. |

00:18:31 | You're right. Five is eighteen degrees. Five and six must add up to what? |

00:18:38 | One eighty. |

00:18:39 | Eighteen plus one seventy-eight. Does that give you one eighty? |

00:18:42 | Oh yeah. |

00:18:44 | Be careful with arithmetic, ladies and gentlemen. |

00:18:53 | Eighteen. One sixty two. One eighty. Perfect. |

00:18:56 | Okay, you're right. Has to be eighteen degrees. |

00:19:01 | What do these- five and six must add up to what number? |

00:19:08 | A hundred and eighty. |

00:19:10 | So if one is eighteen, what is the other one gonna be? |

00:19:15 | One eighty, take away eighteen. |

00:19:17 | Do it- You can do it down here. Do your subtraction. |

00:19:21 | Don't be afraid to have to do subtraction by hand. |

00:19:27 | You sure about this? |

00:19:34 | One eighty minus eighteen. |

00:19:36 | Is only sixty two? Well I'd love to do business with you. |

00:19:39 | Oh. |

00:19:41 | Okay. Number eight- okay. Angle seven is eighteen degrees. |

00:19:46 | Okay, what does angle five have to be? |

00:19:48 | Eighteen degrees. |

00:19:49 | That's right. Okay. |

00:19:52 | And if angle five is eighteen, what does angle- five and six must add up to? |

00:20:04 | A hundred and eighty? |

00:20:05 | So if one's eighteen, what is the other one have to be? What's left? |

00:20:09 | One hundred eighty minus eighteen. |

00:20:15 | Do it. You can do a subtraction here. |

00:20:19 | Okay. You're right- But six and eight are what kind of angles? |

00:20:24 | Supplementary. |

00:20:29 | Oh, vertical angles. |

00:20:30 | And vertical angles are? |

00:20:32 | Hundred and twenty. |

00:20:33 | No. Yeah. Vertical angles are equal. |

00:20:37 | So if six is one sixty-two, eight must also be one sixty-two. |

00:20:43 | Vertical angles must be equal. |

00:20:44 | Oh. All right. |

00:20:46 | Okay? |

00:20:47 | Okay. I know that one and that one are both eighteen degrees |

00:20:51 | and I know that one is one sixty-two 'cause that one is eighteen so would that be one sixty-two? |

00:20:57 | Exactly. 'Cause they're vertical angles and they must be equal. |

00:21:00 | Remember, when you intersect lines, there are two sets of vertical angles. |

00:21:06 | Is this right? |

00:21:07 | No. |

00:21:09 | Okay. |

00:21:10 | I don't understand how to do this. |

00:21:12 | One sixty. |

00:21:13 | Yeah- just check your arithmetic. I lost my pencil. |

00:21:16 | Okay, you know this is eighteen, so this is eighteen, right? |

00:21:20 | If this is eighteen, five and six are a straight angle. |

00:21:24 | What must they add up to? |

00:21:28 | They're supplementary. |

00:21:31 | One eighty? |

00:21:32 | Okay, so one eighty minus the eighteen you already have... |

00:21:38 | gives you one sixty-two. |

00:21:39 | Oh okay. |

00:21:40 | And if this is one sixty- two, then this one must also be... what? |

00:21:44 | One sixty-two. |

00:21:45 | Very good. |

00:21:46 | How would you do this one? |

00:21:48 | Okay, number nine is sixty-three, number eleven is sixty-three. Same way. |

00:21:52 | Okay. |

00:21:53 | Okay. If nine is sixty-three, ten must be one eighty minus sixty-three... |

00:21:59 | Oh okay, I see. |

00:22:01 | and then twelve would be the same as ten. |

00:22:02 | Oh okay. Okay, thank you. Thanks. |

00:22:04 | So then number ten would be? Oh. |

00:22:07 | Ten would have to be one seventeen? |

00:22:09 | Yeah. |

00:22:11 | Thanks, Mr. Thuma. |

00:22:12 | I understand how to do all of this, |

00:22:13 | but I'm not sure what they're asking on number thirty-seven. |

00:22:20 | It's says that there is an angle that has exactly the same measure as its supplement. |

00:22:27 | So it's like the one before? |

00:22:29 | Think about it. Just think a minute. |

00:22:31 | You have two angles that are supplementary which add up to what? |

00:22:36 | One eighty. |

00:22:36 | One eighty. And they're both the same. |

00:22:40 | So they're ninety-degree angles. |

00:22:41 | There you go. |

00:22:42 | Mr. Thuma, what are the- letters for? |

00:22:45 | Don't worry about the letters; that's just identifying points. |

00:22:49 | Remember these are lines. This is line HJ. |

00:22:52 | It's not asking anything about the lines just about the angles. |

00:22:59 | You have a hundred and thirty-six here. Fourteen. What must sixteen be equal to? |

00:23:07 | They're vertical angles. Vertical angles are always ... equal. |

00:23:12 | And fourteen and fifteen must add up to one eighty. |

00:23:17 | Right? They're all the same. These are supplementary. They must add up to one eighty. These are equal. |

00:23:23 | All right. |

00:23:25 | That one. |

00:23:29 | You sure about that? |

00:23:30 | That means one angle is sixty and the supplement would be a hundred and twenty which is not the same measure. |

00:23:37 | Think about it. I'll help you with thirty si-... Yes, that's right. |

00:23:44 | Think 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. |

00:23:54 | I don't get this- Write an equation that represents the sentence, the product- |

00:23:57 | Think about it. What does product mean? |

00:24:02 | Sum means... |

00:24:06 | Let's go over some definitions. Sum means to do what? |

00:24:09 | Add. |

00:24:09 | If I said find the sum. If I said find the difference? |

00:24:14 | Subtract. |

00:24:17 | What does the word product tell you to do? |

00:24:25 | Product is a multiplication problem. |

00:24:34 | Wouldn't you add both of these. |

00:24:39 | No, no. You would add this and this. |

00:24:41 | But if it's- |

00:24:42 | And it's gotta add up to one eighty. |

00:24:44 | But if it's all one big angle wouldn't you add both of them? |

00:24:49 | If you add up all four, you should get three sixty. |

00:24:52 | Is that how it is supposed to be? |

00:24:54 | Yeah, the total should be three sixty. And your arithmetic is off a little bit here. |

00:24:57 | Okay. |

00:25:02 | Is this- |

00:25:03 | Okay, I'm gonna- go over it in a few minutes. |

00:25:08 | No, no, no, no. |

00:25:10 | It says an angle has the same measure as its supplement. |

00:25:14 | That means the two of them, the two angles add up to how much? |

00:25:19 | Hundred eighty. |

00:25:21 | And each one is exactly the same. |

00:25:28 | Think about it. |

00:25:30 | What are two angles that are exactly the same that add up to one eighty? |

00:25:38 | It is one sixty-two? |

00:25:39 | Yes. Yes. |

00:25:41 | How come you told me that it was wrong when I answered the first time? |

00:25:47 | That was what I had the first time and you said it was wrong. |

00:25:49 | No, no. |

00:25:50 | I thought you had sixty-two. |

00:25:52 | No, you had an eight at the end. There was an eight there some place. One seventy-eight or something like that. |

00:26:03 | Okay, do you have the attendance? Did you bubble it? |

00:26:07 | What do you mean which is angle QRS? |

00:26:08 | Well, where is it? |

00:26:17 | Oh, those are- Yes. Somebody came in first period and got them. Thanks. |

00:26:30 | I don't wanna give it away. |

00:26:32 | It is ninety? |

00:26:33 | It's gotta be. Think about it. |

00:26:37 | Look at problem thirty-seven. |

00:26:40 | Two angles are supplementary. |

00:26:42 | Therefore, 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. |

00:26:54 | Each one of them's gotta be... |

00:26:56 | Ninety. |

00:26:57 | ...a ninety degree angle. |

00:27:00 | That's the only way. |

00:27:04 | Do you have a question, Mike? |

00:27:09 | You got it. |

00:27:11 | And we had it before you wrote it on the board. |

00:27:14 | Yes. S cannot be over there. QRS. |

00:27:20 | R must be the vertex. R must be the vertex. |

00:27:23 | Where did you get the T from? |

00:27:25 | I just made that up. It just says as it's supplement. |

00:27:29 | I called the supplement SRT. I just added the next logical letter, right? |

00:27:42 | Where is he going? |

00:27:43 | To the bathroom. |

00:27:44 | Take the wooden pass. |

00:27:49 | Okay. |

00:27:51 | Has anyone- you had a question, Carrie? |

00:27:55 | All right. How- |

00:27:59 | Jay Ho, you can put your cereal box away right now. I know everybody's got that project. |

00:28:04 | Yeah, Ho. Put your cereal box away. |

00:28:06 | Has ... |

00:28:08 | anyone come up, knowing that the product means multiplication? |

00:28:13 | Has anyone come up with the answer to number thirty-eight? |

00:28:18 | What? |

00:28:19 | Yes. |

00:28:21 | No. |

00:28:24 | What did you get, Danielle? |

00:28:28 | No. No, thirty-eight. It says write an equation that represents the sentence, the product of twelve and a number is one ninety-two. |

00:28:38 | Is it twelve K? |

00:28:41 | Twelve K? |

00:28:42 | Twelve and the number K- twelve K... |

00:28:47 | is one ninety-two. |

00:28:50 | Equal sign. |

00:28:53 | Excellent. |

00:28:54 | That's it? |

00:28:55 | That's it. Twelve- doesn't it say the product of twelve and the number K is one hundred ninety-two. |

00:29:04 | Remember, a math equation is just a sentence written with symbols. |

00:29:11 | How many people need a few more minutes on this worksheet? |

00:29:14 | I don't get number thirty-seven. |

00:29:17 | Thirty-seven is ninety degrees. |

00:29:18 | Thirty-seven is two ninety-degree angles. |

00:29:21 | Cool. |

00:29:21 | An angle and it's supplement are the same. They must add up to one eighty... |

00:29:27 | and they're the same. |

00:29:28 | Two ninety degrees? |

00:29:30 | So what is the measure of the angle? The measure of the angle has to be ninety degrees. |

00:29:36 | Right? |

00:29:45 | You can do those last two. |

00:29:47 | Which one? Those- |

00:29:49 | Thirty-nine to forty. |

00:30:00 | Finished. |

00:30:01 | Finished. |

00:30:02 | Okay, you need to measure these. |

00:30:06 | Good. |

00:30:19 | We have time to go over the worksheet from Friday. |

00:30:26 | All right. How many people need a couple extra minutes on this? Carrie, question? |

00:30:35 | Thirty-nine? I know we did integers a couple months ago but come on. |

00:30:40 | I know but I forgot. |

00:30:43 | A negative... |

00:30:47 | No, no, no. Time out. |

00:30:51 | This- |

00:30:55 | I'll answer as soon as everybody is listening. You got confused when I went from addition to multiplication. |

00:31:04 | A negative plus a negative must be? |

00:31:09 | Positive. |

00:31:09 | Negative. |

00:31:10 | Why? |

00:31:12 | A negative times a negative is positive. |

00:31:15 | Okay. |

00:31:16 | But 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? |

00:31:25 | No. |

00:31:26 | No. Danielle. |

00:31:28 | Is number forty-seven, seven? |

00:31:29 | That's correct. The complement of an eighty-three degree angle must be seven. |

00:31:36 | All right. |

00:31:39 | The worksheet we did on Friday after the quiz... we can go over that too today. |

00:31:46 | I don't understand that. |

00:31:47 | You didn't get one, Pat? |

00:31:52 | After the quiz Friday. You didn't pick one up? |

00:31:59 | Were we supposed to- |

00:32:01 | No, but a lot of people did which is why I ran out of copies. This was only supposed to be a class set. |

00:32:11 | Is number forty, seven degrees? |

00:32:13 | Number forty should be seven degrees. Right. |

00:32:16 | I didn't get one. |

00:32:16 | You weren't here Friday? |

00:32:22 | What are we doing tomorrow? |

00:32:23 | Tomorrow, I am going to review everything on angles ... |

00:32:28 | and you're gonna have a quiz on Friday which will be on complementary, supplementary, vertical, all of the stuff that we did today, okay? |

00:32:44 | All 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. |

00:32:56 | Except for the couple of people, I just gave a copy to- let's take a look at them. |

00:33:01 | I didn't do them. |

00:33:03 | After the quiz on Friday. |

00:33:06 | Didn't have time. I didn't do it. |

00:33:08 | I did it. I finished. |

00:33:11 | Things have improved. Haven't they, Meryl? |

00:33:18 | You should have a separate sheet of paper with your answers on it. Yeah. |

00:33:23 | There was only a class set of these, although some people did walk off with them. |

00:33:32 | All right, exercise fifteen asked you ... |

00:33:38 | what was the angle that First Street makes with Main Street? |

00:33:43 | Forty-five. |

00:33:45 | It was a forty-five- degree angle. |

00:33:49 | What is the angle that the property line between the two lots- and the property line ... you have the two lots A and B... |

00:34:02 | Here is Main ... Here is First. |

00:34:06 | I haven't drawn it exact but ... what was the property line- |

00:34:12 | the angle that the property line made with First Street? |

00:34:16 | Now some of you may have measured the acute angle. Some of you may also have measured the... |

00:34:23 | Obtuse. |

00:34:24 | Obtuse angle. What did you get for that angle? |

00:34:26 | For the obtuse angle I got one thirty-four. |

00:34:28 | Okay, so you measured the obtuse angle. Okay? Which came out to? |

00:34:35 | Actually, let's round it off because I think it was supposed to be drawn as an isosceles triangle. Okay? |

00:34:43 | So 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, |

00:34:50 | give or take a degree or two. |

00:34:54 | What is the angle that the property line between the two lots makes with Main Street? That was handed to you. |

00:35:02 | Right, Lindsey? It should have been ninety degrees, right? |

00:35:06 | Could you suggest a more equal way- |

00:35:09 | If I had a piece of property... |

00:35:13 | triangular like this... |

00:35:16 | is this an even way to divide it if I take the midpoint here to the midpoint here, is that giving two equal size lots? |

00:35:24 | No. |

00:35:24 | Joey, how would you divide it up to make it equal? |

00:35:27 | From the middle of First Street... |

00:35:30 | From 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. |

00:35:46 | All right, on exercise thirty-five... |

00:35:51 | How many of you were able to measure those angles and come up very close to seven hundred twenty degrees... within say five? |

00:36:05 | That's all? Only a couple of you? Carrie, how far off were you when you added them up? |

00:36:14 | It's a six-sided piece of property- one, two, three, four- |

00:36:18 | There are six sides. |

00:36:24 | The sum of the angles should be seven hundred twenty degrees. |

00:36:34 | What did you get as a total. John? |

00:36:38 | Seventy-two. |

00:36:42 | Only seventy-two degrees for the six angles? |

00:36:45 | Seven eighteen. |

00:36:47 | Seven eighteen. |

00:36:48 | Oh. Seven eighteen. That's pretty darn close. Within five degrees. How many got seven twenty? Within five degrees. |

00:36:55 | Okay. |

00:36:56 | I got seven twenty exactly. |

00:36:58 | Seven twenty exactly. You were accurate with your protractor. If I move that bottom angle... |

00:37:08 | started out like this, let me see if I can recreate it here for you. |

00:37:13 | One was here, then the line came down here, then went back here. One, two, three, four- this is about what it looked like. |

00:37:20 | This was B, A, F, E, D, and C. |

00:37:29 | If I took ... this angle ... |

00:37:34 | and moved it ... down here ... |

00:37:39 | and made it across this way, moved D down here, should that change the sum- the total of my- |

00:37:47 | Angles? |

00:37:47 | No. |

00:37:48 | It should not. Why? I still have how many angles? Joey. |

00:37:53 | You still have six. |

00:37:54 | I still have six angles. |

00:37:57 | There is a formula and we are gonna go through this after spring break, but I am gonna give you a hint right now. |

00:38:04 | If I take the number of sides ... |

00:38:10 | and I subtract two ... |

00:38:14 | and I multiply that number times one hundred eighty degrees ... |

00:38:21 | that will tell me how many degrees these add up to. |

00:38:25 | How many sides in this figure? |

00:38:27 | Six. |

00:38:29 | How many sides? |

00:38:30 | How many sides in this figure? One, two, three, four, five, six, right? Number of sides, subtract two. |

00:38:39 | Gives me what? |

00:38:40 | Four. |

00:38:40 | Four. What is four times one hundred eighty degrees? |

00:38:47 | Seven hundred twenty. |

00:38:48 | Should be seven hundred twenty, right? How many ... how many degrees should there be in a five-sided figure? |

00:38:58 | A pentagon. |

00:39:02 | Take the formula. Number of sides is five. You don't have to do it in your head. You have pencil and paper. |

00:39:13 | Number of sides is five... |

00:39:16 | Subtract two, and multiply it by one hundred eighty degrees. |

00:39:21 | Five hundred and forty degrees. |

00:39:23 | All five-sided figures contain five hundred forty degrees. |

00:39:31 | Triangle has how many sides? |

00:39:33 | Three. |

00:39:33 | Take away two is one; one times one eighty. |

00:39:36 | A triangle contains eighty degrees. |

00:39:39 | Wouldn't it be one eighty? |

00:39:40 | One hundred eighty degrees. Thank you, Liz. A square. Four sides or rectangle, subtract two is two times one eighty. Three hundred sixty degrees. |

00:39:52 | You 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. |

00:40:07 | How many degrees in a triangle? |

00:40:09 | SOne eighty. |

00:40:10 | One eighty... What is an equilateral triangle? |

00:40:15 | Equal on all sides. |

00:40:16 | Equal on all sides. If an equilateral triangle is equal on all sides, |

00:40:22 | how many degrees are in each angle of an equilateral triangle? Carlos. |

00:40:29 | Sixty. |

00:40:30 | Sixty. It's gotta be sixty, sixty, and sixty. What is an isosceles triangle? |

00:40:36 | It's what we are gonna do tomorrow but we are getting a head start on it. Joey? |

00:40:39 | Two of the angles are the same. |

00:40:42 | Two angles are the same and two... |

00:40:46 | Sides. |

00:40:47 | sides 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? |

00:40:59 | A triangle that doesn't have any of the sides that are the same. |

00:41:02 | None of the sides are equal, right? |

00:41:10 | Tomorrow we are gonna go over triangles ... Friday, tomorrow I will introduce triangles. |

00:41:16 | We're gonna review for the quiz. |

00:41:17 | Your quiz on Friday will contain complementary angles, supplementary angles, vertical angles, and that's about it. Next week... |

00:41:28 | Next week, we're gonna finish this unit. |

00:41:32 | I wanna finish the unit- let me finish and then you can ask- or tell me who is going on vacation early or what. |

00:41:39 | Next week, I want to finish the unit because I don't wanna continue the unit past spring break. |

00:41:45 | The unit test next week will be on Thursday. |

00:41:50 | Because I am afraid some of you may be leaving early for vacation and will not be here on Friday. |

00:41:55 | So 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. |

00:42:04 | But if you're gonna explain it tomorrow, what about the people that are going to Knotts? |

00:42:09 | I am not going to go into any great det- I basically explained to you ... what's going on with trianglescalene, equilateral, isosceles. |

00:42:21 | Just an introduction. |

00:42:24 | The 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? |

00:42:32 | Claudia, two supplementary angles add up to how many degrees? Supplementary. |

00:42:38 | One eighty. |

00:42:39 | One eighty. How can you remember supplementary and complementary and what they add up to? Veronica. |

00:42:47 | Because supplementary- S comes last after C. |

00:42:53 | C comes before S in the alphabet. Ninety comes before one eighty in numbers. Complementary: ninety. Supplementary: one eighty. |

00:43:03 | What can you tell me about vertical angles? |

00:43:07 | Eric. |

00:43:08 | That they're a hundred and eighty. |

00:43:10 | Vertical angles do not necessarily have to be one eighty. |

00:43:17 | Vertical angles must be... |

00:43:21 | Say it, John. Equal. Vertical angles are equal. |

00:43:26 | They must be equal. What is a straight angle? |

00:43:29 | SOne eighty. |

00:43:31 | A right angle. |

00:43:33 | SNinety. |

00:43:34 | An acute angle? |

00:43:35 | SLess than ninety. |

00:43:37 | Less than ninety, greater than zero. Straight angle? |

00:43:42 | SOne eighty. |

00:43:44 | One eighty. Reflex angle? |

00:43:48 | I know. More than one eighty. |

00:43:49 | More than one eighty. How is that possible? |

00:43:52 | It's a circle. |

00:43:52 | If you measure around the opposite way. |

00:44:02 | I can measure this angle two ways. I can measure the inside which would be obtuse, |

00:44:08 | or I can measure it around the outside. That would make this a reflex angle greater than one hundred eighty degrees. |

00:44:17 | Okay, Alba, you had a comment or question you wanted to make before? |

00:44:20 | It was the same one. |

00:44:21 | It was the same one. Okay, how many people are going to Knotts tomorrow? |

00:44:25 | Oh gosh, I'm gonna have a day off. |

00:44:28 | Congratulations. Proud of you. The Knotts Berry Farm trip for all what? Five O's or six O's. |

00:44:35 | And you didn't give me an O either. |

00:44:38 | No, Maryl, I didn't- and you're going? |

00:44:41 | I'm the only one that didn't give you an O? |

00:44:43 | Just kiddin'. |

00:44:44 | Oh 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... |

00:45:03 | Did you get everything you need from it, Danielle? |

00:45:05 | Yeah. |

00:45:06 | Thank you. |

00:45:15 | Okay. You getting this? |

00:45:16 | Yeah. |

00:45:17 | Let me see. Let me see your worksheet. |

00:45:22 | Okay, you got these. Good. |

00:45:23 | I don't get this. |

00:45:25 | Product means multiplication. |

00:45:29 | K is a variable. Remember? The product of twelve ... and a number that's multiplication is... |

00:45:40 | one ninety-two. |

00:45:44 | And a negative plus a negative has to be negative, so this is negative fifty-four. Okay? |

00:46:00 | You can stay in your seat until the bell rings. |

00:46:04 | All done with this, Pat? |

00:46:13 | The quiz Friday will cover no more than we've done- there will be no new information tomorrow for the quiz on Friday. Okay? |

00:46:23 | The next worksheet will not be until Friday after the quiz and it's- it's gonna be on triangles. Carrie. |

00:46:33 | Tomorrow. Yeah, I'll answer all questions tomorrow on angles. I will make sure you understand 'em. |

00:46:39 | So if you understand them- Are you going to Knotts? |

00:46:43 | I got six O's but- |

00:46:45 | But you're not going. Your choice. |

00:46:58 | What school did you come from, Carlos? |

00:47:00 | Inland, right? |

00:47:03 | So you had pretty much all of this before you transferred. Were you an A student in math before you got here? |

00:47:09 | Yeah. |

00:47:10 | Were you? Seems to be. Excuse me, Maryl. |

00:47:14 | I was throwing her back her cereal box. |

00:47:15 | Why can't you hand her back her cereal box? This isn't sixth period. |

00:47:20 | It flies so nice. |

00:47:22 | I said because it flies- |

00:47:23 | It flies so nice. Really nice. |

00:47:28 | I think we have an announcement coming. |

00:47:30 | O: There is an informational meeting today during nutrition, in the lyceum, for all freshmen interested in joining the Vincent Academy next year. |

00:47:41 | It's not you. |

00:47:44 | Freshmen. 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. |

00:47:58 | Okay, you've got about half a minute. If you'd like to line up by the door, you may. |

00:48:14 | Have a good day. |

00:48:16 | Thank you, Jamie. You too. |

00:48:20 | We have no class tomorrow. |

00:48:21 | It's gonna be nice. Five, four, three, two, one, [Bell] bye. |

00:48:30 | SBye, Mr. Thuma. |

00:48:31 | We have to think. All the good people are gonna be gone. |

00:48:34 | That's true. I'm left with the people that don't get the O's. |