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 |
|---|---|
| 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. |