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Triangle Theorems

Added Feb 06, 2023 •

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Triangle Theorems

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what's going on y'all it's your math teacher Miss Harris and I'm back with another video oh my gosh I cannot believe this the last time I'm saying is I'm so sad like you guys I after this video you guys officially be done with your freshman year I like I cannot believe it I'm going to get in this day and I'll get off that be at the end okay today we are going to learn about eq13 triangle congruence so pretty much today and just trying to figure out if these two triangles are congruent if they're equal if they're the same I'm based on their angles sitelink whatever the case maybe see you guys already know what I want you to do go ahead and get your nose I'm going to ride with them to practice with it and let's get into it I hear y'all all right so the main things that you need to save the door for triangle congruence but really there's five but these are mine for a triangle congruence theorems they were talking about today and then want to just the one that I'll show you in a minute so side side side is just went all three corresponding sides are congruent the sign when they're equal okay and that will be indicated by these lines that you see right here so if this one line and let's just say inside one is congruent has died one side who is congruent to that to inside three congruent sides like that pretty much did you see those are both of the triangles you already know that you have side side side angle side which is where two sides and angle between them are all right so once again change my color to you 11 you got this angle in-between that's going to be congruent triangles and leave that side to it can go angle side angle which is where you have two angles and the side in between them are congruent go that you have angle number one congruent to angle number one side one decide one and angle 2 and angle two congruent congruent okay then last but not least two angles and a non-included sides are congruent okay so did you kind of have to watch that one is kind of tricky but I'll show you what to do I'm in just a few minutes so just remember that angle side angle angle angle side you're going to have to go number one and then you're going to have and go number 2 and then you're just randomly going to have one congruent side okay so this one may not really go in order but as long as you see those three indicators you should be able to tell if it's angle angle side or another theorem OK Google to the next one all right understanding congruence congruent sides just mean that the sides are equal to measure like I literally just explained that if she was really tough explain to her if you see the lines that means at your sides are the same okay if you see these little humps right here these little I guess it's parentheses like a better word that you see in between in the triangles that represents an angle this is where congruent angles are going to be equal okay so if you see if I can go with the one in parentheses that mean it's the first thing that's congruent if you see an angle with like two friends see that means that's the second angle that is congruent and very rarely but you may see it you might see three like I said like you're going to see these two but just in case you do this is means that angle number three is congruent okay angles on all right I just congruent triangles do geometric figures are congruent if they have exactly the same size and exactly the same shape okay so no matter whether you turn it if you flip it whatever the case maybe it's going to be congruent does not change the size and it does not change the shape OK do I got examples over here on the left and I've got non-examples over here on the right so once again if you were flagged if you rotate or if you translate which means the squad that shapes it's not going to change the song and it's not going to change what kind of shape that is it is okay aren't here we go next all right so understanding congruent triangles corresponding angles and corresponding sides that are congruent which means they go with me since I'm okay so here in the green you got triangle ABC and if you notice it's got to sign number one. Number two. Number three and a that was also shown you angle number one angle number two and rarely but you will see it sometimes angle number three okay then it's saying that it is congruent to Triangle d e f because you got once again. Number one side number and he's also got angle number one angle number 2 and angle number three so since they have all of these things in common in there in the exact same spot we know that these two triangles are going to be congruent okay so make sure you look for those types now today you may see some triangles that may be reflected you may see them turned a different way whatever the case maybe just make sure you look for the indicators that let you know that those size or those angles are the same that equal all right alright so your order does matter ok so you're corresponding parts have to match and what I mean by that is like when you name your triangle it is okay if you go in a Direction if you go in a certain direction with your name so I can you start today then go to bed then go to see you got triangle ABC right in with the second triangle so if you start with a and end do something here start with D go to eat then go to F don't try to mix up these letters going the exact same direction and that will also help you see side number one. Number one. Number two number three number three angle 2 and angle 3 angle 1 angle 2 and angle 3 so please just understand that your order does matter and your parts have to match okay the weather is translated rotate reflect that whatever the case maybe just make sure I did those things match so that way you can correctly figure out whether side side side side angle side angle side angle angle angle side Stevie Nicks all right so I'm just riding the congruence statement which were really not going to get into but I'll just tell you anyway it's pretty much the same like this is the reason why triangle qrp is going to be congruent to Triangle a CB directions to r p k and then if you flip this when you would see this as a CB they're going in the same direction if you turned it so it's just showing you that everything is in the same spot ringing 31 2 in 2 in and also its angles okay so just make sure you pay attention that please please please and thank you I promise you this practice is going to be really easy your exit is going to be real easy and then we are done with triangle congruence all right so once again your triangle congruence theorems are going to be side to side which means that all three sides of the same side angle side which means you have two congruent sides and one angle that is congruent in between you got angle side angle which is two angles that are and then one side in between a congruent angle angle side which is going to be so if you need to go help out your screen write that down cuz we're going to get the death in just a second all right the side side side once again if three sides of one triangle are congruent to the corresponding sides of another triangle then those triangles are congruent indicators side one side to side 3K then you already know on your triangles are congruent by side side side and you do not have to write the words I just put your bliss and move on so go ahead and Power Rangers great and go ahead and write down this definition for me please and thank you alright let's move on next we're going to have side angle side where if two sides and their included angle in one triangle are congruent to the corresponding sides and included angle of another triangle then those triangles are congruent so pretty much what that means is they have to wear the same size and in the angle in-between that sequel you're going to be good you have side angle side or essay guys to go ahead and write this down on your notes please let Ron all right let's go ahead and move on next you have angle side angle so if two angles and included side of one triangle are congruent to the corresponding angles and included side of another triangle then those triangles are congruent. if you got two angles that are the same and the side in between that it's the same you are going to have a s a congruence okay so go ahead and write this all right let's go ahead and move on to the next one and then angle-angle-side so if two angles and a non-included side of one triangle are congruent to the corresponding angles and non included side of another triangle then those triangles are congruent the pretty much do that two angles that are the same and then one random side that they Mark that it's the same you have angle angle side or a a mess for me and then we will move on are we going I'm going to go ahead and mention the 5th when you're not going to see it much but let me go ahead and explain it it is hypotenuse leg alright so in your nose and what you write this down hypotenuse-leg congruence theorem is if the hypotenuse and the leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle then those triangles are congruent. This when you're not going to see often but you will see this in today's video starts going to go ahead and make you guys aware of it so you. really quick and write that down for me I will go ahead and forward so we can get these done you can do your exit ticket and work okay all right so let me just remind you guys one more time before we get started on question one and two side side side all three sides have to be congruent and they will mark them for you okay side angle side you have two sides that are the same in an angle in between the two sides 2/3 in angle in between an angle in between OK Google side angle you're going to have two angles everything message I forgot to angles and a side in between guy that's what's going to make a congruent and then angle angle side you're going to have two angles but then you're just going to have a random side that will be congruent I said that's a difference a S8 and a s k i n n of course hypotenuse-leg you're going to have a right triangle K and they're also going to have have the hypotenuse be congruent so this longest side right here and then just another leg whether it be play right here or this Lake that I'm working right here they're going to be all right right now all right so number one is triangle jkl congruent to Triangle rst what let's look and see what we have your kind that what we have here on jkl we are given side one side two and side three saying that is congruent to Triangle RC RC we've also got side one tattoo and side three marked as being congruent so since I have three sides that are marked as congruent I know that I'm working with side side side or SSS alright so let's and lucky number two is triangle ABC congruent to triangle DEF well it's looking see we have here I've got one side that can grow in about triangles I've got a second that is congruent to both triangles but I don't have a third side so it can't be side-by-side I don't have any angles that are marked as being congruent I'm only given two things so it's inconclusive since I'm not giving enough information I cannot say that this one is congruent okay it was three and four separate this for y'all do different color do do do do did you get to do all right listen to number three number three is triangle hgj congruent to Triangle kjg let's look and see what we have here okay now we are given a number three that HD in J we have two angles guy that are congruent to the two angles that are in kjg now do you guys think there's not enough information here for both triangles to be proven congruent what actually there is whenever you are given two triangles that are conjoined by side this being the side right here today did they ever share a side we automatically know that is congruent because it's the same size as how the triangles are able to stick together okay so I can mark that as a side that is congruent to angle that are congruent and I have a side that is congruent but now the problem is is that my side is not in between my two angles he is not right here it's over here so I know that I have to have angle angle side right that's going to be my congruent alright that's a good number for change my color ISO number for is triangle ABC congruent to Triangle ADC okay if we have here so we got this right angle I guess that's one angle I've got this angle right here and I've also got a side that they share okay now let's look and see how this plays out switch look at this top Frank and I'll highlight this so that way you guys can see was trying to talk about it so we're just going to look at this triangle right here okay if I go in okay with what I see Mi pan I'm going to start with this anger right here okay so here's the angle here's a side and then here's an angle okay so I know if I'm going to order if I'm looking at what I have of angle side angle or have a essay okay all right number 5 is triangle uvw congruent to Triangle text ywe we have here is another hint that you guys can use if you are ever given and this goes back to a relationship if you are ever given two triangles it like connected a point or a birthday and I'm really referring to right here by you noticed that you have this x right here right and that kind of looks like what we talked about Andy tieu 12 angle relationships as vertical angles and we know vertical angles are going to be congruent they're going to be the same they're going to be equal so I don't actually know I have an angle that is congruent they also know that I have a side that is congruent and I have a second side that is congruent and oh my goodness my my angle is in between my two side so I got a side and angle in a side so I've got SAS going on in this one okay all right listen to number six and change my color alright the number six we got is triangle LMN congruent to Triangle pmn okay good looking what we have here alright so we have a right triangle I'm sorry but we do have a right triangle we have our longest side or hypotenuse K which is congruent we also have a side that we are sharing so we know that that has to also be congruent so we know we have a right angle the hypotenuse is congruent and another leg of this triangle is congruent we know we have the hypotenuse leg congruence theorem OK Google 7 8 9 and 10 I'm going to pause the screen and let you guys try them on your own okay and then we're just going to take them together all right so I'm going to separate 7 and 8 I'm going to pause my screen let you try both and then we are going to check them together all right if we go across your screen and try seven and eight all right here we go so let's start with number 7 all right so number 7 we are given. Number one which is enrollment for giving side number to which is congruent and then we're giving this random angle that is congruent but it's not in between my two sides so it's Ingleside this is technically going to be so I'd side angle but we don't have a side side angle over here so this one cannot be congruent okay so I'll see if you got that right if you didn't that's okay you got plenty more chances to pray looks like the number eight number 8 says is triangle qt are congruent to Triangle Str well let's look and see what we have okay so I know I've got this first angle which is congruent I've got this right angle okay cuz I have a right triangle and then I also have a side that they share okay so I know that's going to work all right so now I need to look at what do I have look at the order that you're going in you have an angle you have an angle and you have a side so angle-angle-side or aaas nice of ya  right awesome awesome job if not that's okay you can try practicing again on numbers 9 and 10 if we go number 9 is triangle QRS T and throw it to Triangle T Askew and number 10 is triangle jkm congruent to Triangle Q p.m. so I want you guys to pause your screen separate these for going to try them and then we will check them together if we go out your screen and try numbers 9 + 10 9 + 10 / 9 we noticed that we have this side that is congruent I we also know that we have a shared side and we don't share size are shared sides are also congruent and then we also know that we have this angle right here in this angle right here okay now don't think this was given to you guys I'm going to give it to you now that they are congruent so this is going to be side angle side and the same thing for number and I don't feel like they gave enough information but it's honest answer keys and I'm looking at right now so I'm going to go ahead and give you what information they gave me they're telling me that these two sides are congruent angle and an angle an angle with me we're going to have a essay to do with only four problem so if you got to go ahead and get that done and make sure that you email it to me and here is k r. R. Net and it is finally time for me to get oh it's not oh I have three more to practice with it's a piece but not yet not time for me to get sad listen to disperse once opposed side a b is congruent to side CD and angle b a c is congruent angle DCA DC I bring here kinda got this shared side so what I'm looking at is a side angle inside Choice be next one I'm right here we got a side we've got another side and then we also got an angled oh my goodness look another side and ghost die and last but not least this time we're given angle measure side length measures I'm sorry so you got a side that's congruent Stardust congruence and another side that is congruent I should have another shape that means that this was going to be side-side-side all right now I think it's time for me to get that was saying at the beginning of this video I am so I'm sad this is my last video so so sad I cannot believe that you guys are done with your freshman year I feel like this year has went by really slow but also flew by like I cannot believe that you guys are now sophomores but I'm not going to go too much of your time I just want to let you guys know that I love and I'm so so so so so proud of you for being self-motivated or getting your work done returning it in for trying to maintain the best grade as possible on the school year I know it's been a lot with this pandemic I know it's been a lot with this this morning but I truly truly truly thank you guys enough a job for hanging in there with me this entire school year I know we most of us isn't have never met face-to-face some of y'all I have talked before in previous years but no matter what you are my baby and I love you all and I'm so proud of you for making it through this year if you meet me you guys already know what to do you can always email me a hairstyle that rcschool.net you're always free to stay in my remind app I do not mind I'm going to use every single year so even if you just want to take a Break Stuff Limp gray stuffed in your stuff I don't care that's what I'm here for I'm always here to help you guys like I said I love you so much I hope you have a great rescue you here as in like a week left two weeks left if that enjoy your summer and enjoy yourself for Junior and Senior year it will fly by and before you know it you'll be turn off this stage but please know I'm always here and I love you. Okay I'll see y'all later bye

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Triangle Theorems

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