00:0-1 | Yeah , Here's the final part to grade nine . | |

00:01 | Math in an hour . So it's kind of going | |

00:03 | to end up taking a little bit longer an hour | |

00:04 | to get through all three . But this is definitely | |

00:06 | the shortest section . I should be able to do | |

00:07 | this section in under 10 minutes . This section is | |

00:09 | on geometry . So the geometry section , um , | |

00:12 | I'm just gonna quickly go through these topics for part | |

00:14 | three of grade nine math in an hour . So | |

00:17 | this has been the last year you would have done | |

00:19 | . You probably would've started by reviewing parallel line theorems | |

00:21 | . You probably already know these from grade eight , | |

00:24 | but parallel line themes . Basically , if you have | |

00:26 | two parallel lines , we can tell the parallel because | |

00:28 | these little arrows here we have two parallel lines that | |

00:30 | are cut by a transfer cell . Um , there | |

00:33 | are some theorems we can use to find unknown angles | |

00:35 | . So first theorem is the alternate into your angles | |

00:39 | theorem , and that tells us if we have this | |

00:41 | Z pattern , the angles inside the Z are equal | |

00:45 | to each other . Also , there's the F pattern | |

00:47 | . We call those corresponding angles the corresponding angle theorem | |

00:51 | the angles inside the f are also equal to each | |

00:54 | other . And lastly , we have the C pattern | |

00:56 | we call those co interior angles and the angles inside | |

01:00 | of a C . They're not equal to each other | |

01:01 | , but they do add to 1 80 so we | |

01:04 | can use those three theorems in combination with supplementary angles | |

01:07 | and , um , opposite angles . Remember , opposite | |

01:09 | angles like this angle here in this angle here are | |

01:12 | equal to each other . We can use these theorems | |

01:14 | to be able to figure unknown angles if we have | |

01:16 | parallel lines . So if we have here two parallel | |

01:19 | lines , this tells us they're parallel . Um , | |

01:22 | let's find these three unknown angles using our parallel line | |

01:25 | theorems . Well , first of all , here's A | |

01:27 | is opposite from the 75 degrees , and we know | |

01:30 | opposite angles are equal . So I know is equal | |

01:32 | to 75 degrees , and we could stay off the | |

01:35 | side here . They're opposite angles . And that's how | |

01:36 | we know . Um , what's find ? Let's find | |

01:40 | the next will be . Look at this F pattern | |

01:44 | here . I've got an F pattern . I know | |

01:46 | angles inside the F pattern are equal to each other | |

01:48 | , so I know B is equal to 75 degrees | |

01:53 | as well . And there's lots of ways I could | |

01:55 | know what angle C is . Um , I could | |

01:57 | see an F pattern here , so I know a | |

01:59 | is equal to see . Um I know B and | |

02:02 | C are opposite , so I know B and C | |

02:03 | are equal to each other , or I can look | |

02:05 | at the Z pattern here , so they're alternate interior | |

02:08 | angles . These two angles are equal , so I | |

02:10 | know , see is also equal to 75 degrees . | |

02:15 | Next thing you would have looked at probably is Pythagorean | |

02:17 | theorem . Pythagorean theorem can only be used when you | |

02:20 | have a right triangle in a right triangle is a | |

02:22 | triangle has one angle equal to 90 degrees , and | |

02:25 | we can tell because there's this little rectangle inside marking | |

02:28 | off that there is a 90 degree angle , Um | |

02:33 | , in a right triangle , one of the sides | |

02:35 | we call the hypothesis . How do we know which | |

02:37 | side that is ? Well , it's always the longest | |

02:40 | side of the right triangle , and if you can't | |

02:42 | tell which one is the longest we know , it's | |

02:43 | always decide that is opposite from the right angle . | |

02:47 | It's always the side across from the right angle and | |

02:50 | what is Pythagorean theorem . Pythagorean theorem tells us that | |

02:54 | the sum of the squares of the shorter two sides | |

02:56 | so the square of the shorter two sides . If | |

03:00 | we add up those areas , it should equal exactly | |

03:05 | the area of the square of the larger side . | |

03:08 | Algebraic Lee speaking . We say a squared plus B | |

03:10 | squared equals C squared where A and B represent the | |

03:13 | shorter two sides and we sometimes call those the legs | |

03:16 | and the C represents the longest side . We call | |

03:18 | that the high pot news , so Pythagorean theorem to | |

03:21 | sum of the squares of the shorter two sides . | |

03:23 | So a squared plus B squared is equal to the | |

03:25 | square of the longer side . C squared well , | |

03:27 | to practice using Pythagorean theorem , it can be used | |

03:30 | to find an unknown side of a right triangle as | |

03:33 | long as we know two of the other sides . | |

03:35 | So for this triangle here we have our right angle | |

03:38 | here , which makes the side opposite that right angle | |

03:42 | are hypotenuse and we always use the letters C for | |

03:44 | the hypotenuse and we use the letters A and B | |

03:48 | for the shorter two sides . Doesn't matter which is | |

03:50 | which , but we know that the figurine theorem is | |

03:52 | true for all right . Triangle . So a squared | |

03:54 | plus B squared equals C squared . We can use | |

03:57 | this formula to figure out the unknown side sea by | |

03:59 | plugging into our Formula nine squared . Plus 12 squared | |

04:04 | gives us C squared for evaluate . Nine squared plus | |

04:08 | 12 squared . We would get to 25 . That's | |

04:10 | what C squared is equal to . But to figure | |

04:12 | what C is equal to , we have to isolate | |

04:14 | . See by moving the square to the other side | |

04:15 | . The opposite of squaring is square rooting . So | |

04:18 | I have to square root 2 . 25 to get | |

04:21 | me c squared up to 25 . What times itself | |

04:24 | is equal to to 25 . Well , that's 15 | |

04:27 | , so c equals 15 . So we would say | |

04:29 | c equals 15 and we are in meters . So | |

04:32 | I should write meters beside that here . What if | |

04:35 | the missing side is one of the legs ? So | |

04:37 | once again , right angle opposite . That is a | |

04:39 | hypothesis that c So our legs are here and here | |

04:43 | . If I used to Failure and theorem a squared | |

04:45 | plus B squared equals c squared . My unknown this | |

04:48 | time is the B . So I could start by | |

04:51 | rearranging the formula , or I could plug in and | |

04:53 | then rearrange I'm gonna plug in first . So I | |

04:56 | know A is 5454 squared plus B squared equals C | |

05:01 | squared +90 C . Is 10.3 . And now what | |

05:04 | I'm going to want to do is isolate the B | |

05:06 | squared by moving the 5.4 square to the other side | |

05:09 | so I b squared equals 10.3 squared minus 5.4 squared | |

05:16 | d squared . If I evaluate that , I get | |

05:19 | 76.93 and then if I take sorry , that's B | |

05:23 | squared to get B , I have to actually square | |

05:27 | root to 76 93 and that gives me an approximate | |

05:35 | answer . I should write approximately here because I've rounded | |

05:38 | this answer . If I evaluate that , I get | |

05:41 | 8.77 8.77 all right , And what units are we | |

05:49 | in centimetres ? Okay , so that's Pythagorean theorem . | |

05:53 | The next thing you probably looked at is three dimensional | |

05:57 | shapes getting surface area and volume of three D shapes | |

06:00 | . I'm sure you remember what the difference between volume | |

06:02 | surface area , so let's just go into a couple | |

06:04 | of quick calculations . Let's start with a couple of | |

06:06 | different prisms . Um , here's a rectangular prism . | |

06:08 | It's a rectangular prism because the base of it is | |

06:12 | a rectangle . Let's find the volume of this rectangular | |

06:15 | prison . It's a volume of any prism is actually | |

06:18 | just equal to area of days multiplied by the height | |

06:25 | of the prison . And since the base of this | |

06:27 | shape is just a rectangle , let's find the area | |

06:30 | of the rectangle by doing its length times its width | |

06:33 | so length , times width and multiply that by the | |

06:35 | height of the entire prison . So L W H | |

06:39 | is the volume of this rectangular prism . We could | |

06:43 | get that formula from our Formula Page Rectangular prism volume | |

06:47 | area based on site , which is length , times | |

06:49 | , weight , times site . So if we evaluate | |

06:51 | this volume equals nine times seven time 16 , we | |

06:57 | would figure out volume is 1000 and eight centimetres . | |

07:03 | Cute member of volume is always in units Cube . | |

07:08 | Here we have a triangular prison . Let's find the | |

07:10 | volume of this as well . Members always area base | |

07:12 | times height , so the base is a triangle . | |

07:14 | So I'm gonna need to find the area of that | |

07:16 | triangle area of a triangle is base times height divided | |

07:18 | by two . And we call the base of the | |

07:20 | triangle of the triangle B , and we call the | |

07:22 | height of the triangle . Actually call it El because | |

07:24 | we need to use H for the height of the | |

07:26 | prison . So we're going to have to do the | |

07:28 | times all divided by two , and then multiply that | |

07:30 | by h . So our formula for volume of of | |

07:32 | a triangular prism is B l h divided by two | |

07:36 | . If we plug that into our formula 23 times | |

07:41 | 34 times H , which is 4.8 , divide the | |

07:47 | entire product by two . And if we do that | |

07:51 | , I'll just write my answer below . Here we | |

07:54 | get 18 768 m . Cute . And lastly , | |

08:03 | I have a sphere . So this one is not | |

08:06 | a prism . Um , but for a sphere , | |

08:08 | let's instead of finding volume this time , let's find | |

08:11 | let's find the surface area this time . Surface area | |

08:14 | for a sphere , it's four pi r squared . | |

08:16 | We can look at our Formula page surface area four | |

08:19 | pi r squared . So we're gonna find the surface | |

08:21 | area of this sphere for pie . Our square . | |

08:26 | Remember , R stands for the radius , which is | |

08:28 | a distance from the center of the sphere to the | |

08:30 | edge . If it gave us the diameter , we | |

08:33 | would have to divide it by two . But it | |

08:35 | gives us the radius in this question , so just | |

08:37 | plug in our radius . So four pi times 28 | |

08:42 | squared and make sure you press the pie button on | |

08:44 | your calculator . Don't use 3.14 Approximate value calculator stores | |

08:48 | many more digits for its pi value , so you | |

08:51 | know more accurate answer if you actually use the pie | |

08:53 | button on your calculator . So if we do four | |

08:56 | pi times 28 squared , make sure if you're doing | |

08:59 | this step by step , you're following bed Mass . | |

09:02 | But if you're typing it on a scientific calculator , | |

09:05 | it'll do the correct order of operations here for you | |

09:07 | , and we will get 98 52 0.3 In this | |

09:15 | case , we are in millimeters squared . Remember Surface | |

09:19 | area . It's always in units squared volume . It's | |

09:22 | always in units . Cute . So 9008 . 52.3 | |

09:28 | millimeters squared . So probably lastly in your geometry course | |

09:33 | you would have done some optimizing measurements . I'm not | |

09:36 | gonna have time to get through that because I think | |

09:37 | I'm already over an hour . But these are the | |

09:40 | main concept you would have done in geometry . Some | |

09:42 | service area volume , calculations , um , without your | |

09:45 | into your room and parallel line theorems . So that's | |

09:50 | it for grade nine . Math in an hour . | |

09:51 | Hopefully , you watched all three parts and you're ready | |

09:54 | for your math exam ? Um , yeah , and | |

09:57 | that's it . |

#### DESCRIPTION:

Here is a great exam review video reviewing all of the main concepts you would have learned in the MPM1D grade 9 academic math course. The video is divided in to 3 parts. This is part 3: Geometry. In this video you will review parallel line theorems, pythagorean theorem, and volume/surface area of three dimensional shapes.

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ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 3) is a free educational video by Lumos Learning.

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