00:00:02  What is the angle that is vertical to the seventydegree 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  Fiftythree degrees. 
00:01:27  Okay. Two things. You have fiftythree 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  Thirtyseven. 
00:01:45  Thirtyseven degrees, right? 
00:01:50  Why thirtyseven degrees, Jamie? 
00:01:54  Carrie? 
00:01:55  Because thirtyseven and fiftythree equals ninety. 
00:01:59  Thirtyseven and fiftythree 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 sixtydegree 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 thirtydegree 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 thirtyeight 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 thirtyeight degrees... 
00:06:46  Fiftytwo. 
00:06:47  Thank you, Tracy. 
00:06:50  If I have an angle of thirtyeight degrees, what is ninety minus thirtyeight? 
00:06:55  Fiftytwo. 
00:06:57  Fiftytwo. So the complement would be fiftytwo degrees. Right? 
00:07:02  What's the complement of an angle of seven degrees? Ho? 
00:07:05  Eightythree. 
00:07:06  Eightythree. 
00:07:07  The complement of an angle of eightyfour, 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  Seventynine degrees. 
00:07:24  Number five. Joey? 
00:07:26  Thirtythree. 
00:07:28  Sure about that? Claudia? 
00:07:30  Twenty 
00:07:30  Twentythree. Gotta be careful with the arithmetic. Number six. 
00:07:35  Jamie. 
00:07:36  Sixtyone degrees. 
00:07:38  Good. Number seven. Veronica. 
00:07:42  Thirtyseven. 
00:07:43  Thirtyseven. Number eight. Crystal. 
00:07:47  Fortyfour degrees. 
00:07:47  Fortyfour is good. Number nine. That is a tough one. Meryl. 
00:07:51  Eightynine. 
00:07:52  All right. Number ten. 
00:07:55  Ho. 
00:07:56  Thirtyeight. 
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  Fortyfive. 
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 seventyeight. 
00:08:38  One seventyeight. 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  Seventynine. 
00:08:47  Seventynine. Okay, Michelle, number fifteen. 
00:08:52  Eightyeight. 
00:08:52  Eightyeight. 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 eightytwo. Carrie. 
00:09:08  Ninetyeight. 
00:09:09  Ninetyeight 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 sixtyfive. 
00:09:20  A hundred and sixtyfive. Perfect. Number eighteen. 
00:09:26  Patricia. 
00:09:27  One fortyfive. One fortyfive. 
00:09:29  Number eighteen, a hundred and fortyfive is a little high. 
00:09:35  Fortyfive. 
00:09:36  Fortyfive. That will work. Number nineteen. 
00:09:41  Alba. 
00:09:43  A hundred and thirtysix. 
00:09:44  A hundred and thirtysix. Number twenty. 
00:09:47  Arelia. 
00:09:49  Thirtyone. 
00:09:50  Thirtyone. Number twentyone. John. 
00:09:54  Twelve. 
00:09:55  Twelve degrees. Number twentytwo. Do we get everybody? Mike. 
00:09:59  Six degrees. 
00:10:00  Six degrees. Carlos, number twentythree. 
00:10:04  Hundred twentyone. 
00:10:04  One twentyone. 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 fortyone degrees. How many people got somewhere around there? Fortyone plus or minus? 
00:11:04  I got fortyseven. 
00:11:05  Fortyseven? 
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 fiftyfour degrees. 
00:11:26  Fiftyfive. 
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 fortydegree 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 eightythreedegree angle? 
00:11:48  Alba? 
00:11:49  Seven degrees. 
00:11:50  Seven degrees. Jamie, what about the complement of a sixteendegree angle? 
00:11:54  Eightyfour? 
00:11:57  Seventyfour. 
00:11:58  Seventyfour. Okay. The supplement of a seventyfivedegree angle. Ho. 
00:12:04  One O five. 
00:12:06  Supplement of a hundred and thirtydegree 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 fivedegree angle? 
00:12:18  Danielle? 
00:12:19  One seventyfive. 
00:12:20  One seventyfive. 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 warmup. 
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 warmup. 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 thirtyseven and thirtyeight, 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  Ninetytwo? 
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 seventyeight. 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 sixtytwo, eight must also be one sixtytwo. 
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 sixtytwo 'cause that one is eighteen so would that be one sixtytwo? 
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 sixtytwo. 
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 sixtytwo. 
00:21:45  Very good. 
00:21:46  How would you do this one? 
00:21:48  Okay, number nine is sixtythree, number eleven is sixtythree. Same way. 
00:21:52  Okay. 
00:21:53  Okay. If nine is sixtythree, ten must be one eighty minus sixtythree... 
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 thirtyseven. 
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 ninetydegree 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 thirtysix 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 thirtyseven and thirtyeight. 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 sixtytwo? 
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 sixtytwo. 
00:25:52  No, you had an eight at the end. There was an eight there some place. One seventyeight 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 thirtyseven. 
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 thirtyeight? 
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, thirtyeight. It says write an equation that represents the sentence, the product of twelve and a number is one ninetytwo. 
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 ninetytwo. 
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 ninetytwo. 
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 thirtyseven. 
00:29:17  Thirtyseven is ninety degrees. 
00:29:18  Thirtyseven is two ninetydegree 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  Thirtynine 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  Thirtynine? 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 twentysix steps backwards ... and then I take another twentyeight 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 fortyseven, seven? 
00:31:29  That's correct. The complement of an eightythree 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 thirtyfive... 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  Fortyfive. 
00:33:45  It was a fortyfive 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 thirtyfour. 
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 thirtyfive. We've got fortyfive here. This also should have been a fortyfive 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 thirtyfive... 
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 sixsided 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  Seventytwo. 
00:36:42  Only seventytwo 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 fivesided 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 fivesided 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 ninetytwo. 
00:45:44  And a negative plus a negative has to be negative, so this is negative fiftyfour. 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.
